Level-Spacing Distributions and the Airy Kernel

Abstract

Scaling level-spacing distribution functions in the ``bulk of the spectrum'' in random matrix models of $N\times N$ hermitian matrices and then going to the limit $N\to \infty$, leads to the Fredholm determinant of the sine kernel $\sin \pi (x-y)/\pi (x-y)$. Similarly a scaling limit at the ``edge of the spectrum'' leads to the Airy kernel $[\mathrm{Ai}(x){\mathrm{Ai}}^{\prime }(y)-{\mathrm{Ai}}^{\prime }(x)\mathrm{Ai}(y)]/(x-y)$. In this paper we derive analogues for this Airy kernel of the following properties of the sine kernel: the completely integrable system of P.D.E.'s found by Jimbo, Miwa, M{ô}ri and Sato; the expression, in the case of a single interval, of the Fredholm determinant in terms of a Painlev{é} transcendent; the existence of a commuting differential operator; and the fact that this operator can be used in the derivation of asymptotics, for general $n$, of the probability that an interval contains precisely $n$ eigenvalues.

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References in corpus (2)

• Level-Spacing Distributions and the Airy Kernel
• Introduction to Random Matrices

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• Higher Order Analogues of Tracy-Widom Distributions via the Lax Method
• Riemann-Hilbert problems for last passage percolation
• Edge scaling of the β-Jacobi ensemble
• Large fluctuations of the area under a constrained Brownian excursion
• Reflective prolate-spheroidal operators and the KP/KdV equations
• The crossing probability for directed polymers in random media
• Numerical study of a multiscale expansion of the Korteweg de Vries equation and Painlevé-II equation
• Direct Evidence for Universal Statistics of Stationary Kardar-Parisi-Zhang Interfaces
• Third-order phase transition: random matrices and screened Coulomb gas with hard walls
• On Wright's generalized Bessel kernel
• Hessian eigenvalue distribution in a random Gaussian landscape
• Edge Universality for Orthogonal Ensembles of Random Matrices
• Gap probability of the circular unitary ensemble with a Fisher-Hartwig singularity and the coupled Painlevé V system
• Growth models, random matrices and Painleve transcendents
• TASEP and generalizations: Method for exact solution
• Reggeometry of deeply virtual Compton scattering (DVCS) and exclusive vector meson production (VMP) at HERA
• Edge scaling limit of the spectral radius for random normal matrix ensembles at hard edge
• Gaussian unitary ensemble with jump discontinuities and the coupled Painlevé II and IV systems
• An elementary introduction to the geometry of quantum states with pictures
• Spectral Properties of the Jacobi Ensembles via the Coulomb Gas approach
• Analysis of etching at a solid-solid interface
• Log-Gamma directed polymer with fixed endpoints via the replica Bethe Ansatz
• Exact Solution of the Landau-Lifshitz Equations for a Radiating Charged Particle in The Coulomb Potential
• Supremum of the Airy2 process minus a parabola on a half line
• First Passage Time for Many Particle Diffusion in Space-Time Random Environments
• Bispectrality and Time-Band-Limiting: Matrix valued polynomials
• Truncated linear statistics associated with the eigenvalues of random matrices II. Partial sums over proper time delays for chaotic quantum dots
• Kardar-Parisi-Zhang Interfaces with Curved Initial Shapes and Variational Formula
• Maximum of an Airy process plus Brownian motion and memory in KPZ growth
• Circular Kardar-Parisi-Zhang interfaces evolving out of the plane
• Level Spacing Distribution of Critical Random Matrix Ensembles
• Integrable operators and the squares of Hankel operators
• Intermediate disorder directed polymers and the multi-layer extension of the stochastic heat equation
• The hard edge tacnode process and the hard edge Pearcey process with non-intersecting squared Bessel paths
• Classical integrability for beta-ensembles and general Fokker-Planck equations
• Subgap states in disordered superconductors with strong magnetic impurities
• Enhanced stability and chaotic condensates in multi-species non-reciprocal mixtures
• Shocks, rarefaction waves, and current fluctuations for anharmonic chains
• Noncolliding Brownian Motion with Drift and Time-Dependent Stieltjes-Wigert Determinantal Point Process
• Finite-temperature and finite-time scaling of the directed polymer free-energy with respect to its geometrical fluctuations
• Free energy distribution of the stationary O'Connell-Yor directed random polymer model
• The lower tail of the half-space KPZ equation
• $1/f^{\alpha }$ power spectrum in the Kardar-Parisi-Zhang universality class
• Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues
• Role of the Tracy-Widom distribution in the finite-size fluctuations of the critical temperature of the Sherrington-Kirkpatrick spin glass
• Random matrices, free probability and the invariant subspace problem relative to a von Neumann Algebra
• Zero-temperature spinglass-ferromagnetic transition : scaling analysis of the domain-wall energy
• KPZ statistics of second class particles in ASEP via mixing
• Low-temperature entropy in JT gravity
• A PDE for the joint distributions of the Airy Process
• A limit theorem at the spectral edge for corners of time-dependent Wigner matrices
• The 1999 Heineman Prize Address- Integrable models in statistical mechanics: The hidden field with unsolved problems
• Relationships between $\tau$-function and Fredholm determinant expressions for gap probabilities in random matrix theory
• Super-sharp resonances in chaotic wave scattering
• Exact equivalences and phase discrepancies between random matrix ensembles
• On the principal components of sample covariance matrices
• On two-time distribution functions in (1+1) random directed polymers
• Uniform tail asymptotics for Airy kernel determinant solutions to KdV and for the narrow wedge solution to KPZ
• Hallmarks of the Kardar-Parisi-Zhang universality class elicited by scanning probe microscopy
• Bethe Ansatz in the Bernoulli Matching Model of Random Sequence Alignment
• Step fluctuations for a faceted crystal
• On Finite Rank Deformations of Wigner Matrices
• $N$-point free energy distribution function in one dimensional random directed polymers
• Dyson's constant for the hypergeometric kernel
• Universal edge scaling in random partitions
• Spiked Models in Wishart Ensemble
• Partial yet definite emergence of the Kardar-Parisi-Zhang class in isotropic spin chains
• Brownian flights over a circle
• Extreme Eigenvalue Distributions of Jacobi Ensembles: New Exact Representations, Asymptotics and Finite Size Corrections
• Spiked separable covariance matrices and principal components
• Inflation as an Information Bottleneck - A strategy for identifying universality classes and making robust predictions
• Non-intersecting Paths, Random Tilings and Random Matrices
• On the Increasing Tritronquée Solutions of the Painlevé-II Equation
• On the partial connection between random matrices and interacting particle systems
• Random walks and random fixed-point free involutions
• A Survey on the Eigenvalues Local Behavior of Large Complex Correlated Wishart Matrices
• From gap probabilities in random matrix theory to eigenvalue expansions
• Anisotropic local laws for random matrices
• The master Painlevé VI heat equation
• Tracy-Widom limit of q-Hahn TASEP
• Convergence rates of the spectral distributions of large random quaternion self-dual Hermitian matrices
• On the limit of extreme eigenvalues of large dimensional random quaternion matrices
• The gap probabilities of the tacnode, Pearcey and Airy point processes, their mutual relationship and evaluation
• Structure of trajectories of complex matrix eigenvalues in the Hermitian-non-Hermitian transition
• Nonlinear amplification of coherent waves in media with soliton-type refractive index pattern
• Asymptotic forms for hard and soft edge general $\beta$ conditional gap probabilities
• On the Scaling Limits of Determinantal Point Processes with Kernels Induced by Sturm-Liouville Operators
• Spectra of Random Hermitian Matrices with a Small-Rank External Source: The critical and near-critical regimes
• A Brownian Motion Model of Parametric Correlations in Ballistic Cavities
• Distribution of a particle's position in the ASEP with the {alternating} initial condition
• The mean field theory of spin glasses: the heuristic replica approach and recent rigorous results
• Lyapunov exponent, universality and phase transition for products of random matrices
• Asymptotics for random Young diagrams when the word length and alphabet size simultaneously grow to infinity
• Transition between characters of classical groups, decomposition of Gelfand-Tsetlin patterns and last passage percolation
• Distribution Functions for Edge Eigenvalues in Orthogonal and Symplectic Ensembles: Painlevé Representations II
• Crossover between various initial conditions in KPZ growth: flat to stationary
• On the Largest Singular Values of Random Matrices with Independent Cauchy Entries
• The hard-edge tacnode process for Brownian motion
• Limiting Statistics of the Largest and Smallest Eigenvalues in the Correlated Wishart Model
• Supersymmetry Method for Chiral Random Matrix Theory with Arbitrary Rotation Invariant Weights
• Darboux transformations and random point processes
• Unitary matrix models and random partitions: Universality and multi-criticality
• Gap probabilities for the Generalized Bessel process: a Riemann-Hilbert approach
• Non-Perturbative Random Matrix Model of $\mathcal{N}=2$ JT Supergravity
• Monotonous subsequences and the descent process of invariant random permutations
• Tracy-Widom distribution as instanton sum of 2D IIA superstrings
• Breaking supersymmetry in a one-dimensional random Hamiltonian
• Oscillatory asymptotics for the Airy kernel determinant on two intervals
• Universal behavior of the full particle statistics of one-dimensional Coulomb gases with an arbitrary external potential
• Brownian Gibbs property for Airy line ensembles
• A Stirling-type formula for the distribution of the length of longest increasing subsequences
• Singular value decomposition of large random matrices (for two-way classification of microarrays)
• Finite GUE distribution with cut-off at a shock
• Random walk on nonnegative integers in beta distributed random environment
• Density of States in a Mesoscopic SNS Junction
• Universality for multiplicative statistics of Hermitian random matrices and the integro-differential Painlevé II equation
• Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case
• Universality for directed polymers in thin rectangles
• Universal halting times in optimization and machine learning
• Extended Quantum Color Coding
• Exact solution of the Bernoulli matching model of sequence alignment
• Quasi-linear Stokes phenomenon for the Hastings-McLeod solution of the second Painlevé equation
• Efficient computation of cumulant evolution and full counting statistics: application to infinite temperature quantum spin chains
• On Some Applications of Sakai's Geometric Theory of Discrete Painlevé Equations
• Quickest Online Selection of an Increasing Subsequence of Specified Size
• Critical behavior in topological ensembles
• Global Asymptotics for the Christoffel-Darboux Kernel of Random Matrix Theory
• Why random matrices share universal processes with interacting particle systems?
• Convergence rate to the Tracy-Widom laws for the largest eigenvalue of Wigner matrices
• Double scaling limit in the random matrix model: the Riemann-Hilbert approach
• Finite size effects and loss of self-averageness in the relaxational dynamics of the spherical Sherrington-Kirkpatrick model
• On statistical models on super trees
• Product matrix processes as limits of random plane partitions
• Exact time evolution formulae in the XXZ spin chain with domain wall initial state
• Spectral gene set enrichment (SGSE)
• Differential equations for the KPZ and periodic KPZ fixed points
• Emptiness formation probability of the six-vertex model and the sixth Painlevé equation
• Universal exit probabilities in the TASEP
• Height distributions in competitive one-dimensional Kardar-Parisi-Zhang systems
• Sample canonical correlation coefficients of high-dimensional random vectors with finite rank correlations
• Vicious Walkers and Hook Young Tableaux
• Limiting current distribution for a two species asymmetric exclusion process
• Asymptotics of Plancherel measures for symmetric groups
• Tracy-Widom GUE law and symplectic invariants
• Painleve formulas of the limiting distributions for non-null complex sample covariance matrices
• Scaled limit and rate of convergence for the largest eigenvalue from the generalized Cauchy random matrix ensemble
• Fluctuations in the discrete TASEP with periodic initial configurations and the Airy_1 process
• Width and extremal height distributions of fluctuating interfaces with window boundary conditions
• Solution of the Kolmogorov equation for TASEP
• On the frequencies of patterns of rises and falls
• Decomposition of spectral density in individual eigenvalue contributions
• KPZ fluctuations in finite volume
• Fluctuations for stationary $q$-TASEP
• Entanglement Hamiltonian of a nonrelativistic Fermi gas
• Arctic curves of the four-vertex model
• Permutations avoiding 312 and another pattern, Chebyshev polynomials and longest increasing subsequences
• Asymptotic Theory of Eigenvectors for Random Matrices with Diverging Spikes
• PDEs satisfied by extreme eigenvalues distributions of GUE and LUE
• $T\overline{T}$-deformed free energy of the Airy model
• Airy process with wanderers, KPZ fluctuations, and a deformation of the Tracy--Widom GOE distribution
• Hidden diagonal integrability of $q$-Hahn vertex model and Beta polymer model
• Gap probability for the hard edge Pearcey process
• Some Universal Properties for Restricted Trace Gaussian Orthogonal, Unitary and Symplectic Ensembles
• A smooth transition towards a Tracy-Widom distribution for the largest eigenvalue of interacting $k$-body fermionic Embedded Gaussian Ensembles
• Tail decay for the distribution of the endpoint of a directed polymer
• Discrete orthogonal polynomial ensembles and the Plancherel measure
• Finite-rank perturbations of random band matrices via infinitesimal free probability
• Unzipping of two random heteropolymers: Ground state energy and finite size effects
• Orthonormal Polynomials on the Unit Circle and Spatially Discrete Painlevé II Equation
• A phase transition for non-intersecting Brownian motions, and the Painleve II equation
• Ground-state energy distribution of disordered many-body quantum systems
• Spectral rigidity for addition of random matrices at the regular edge
• A GUE Central Limit Theorem and Universality of Directed First and Last Passage Site Percolation
• Semiclassical electron transport at the edge of a 2D topological insulator: Interplay of protected and unprotected modes
• An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model
• Domain wall fluctuations of the six-vertex model at the ice point
• On the Tracy-Widom${}_{\beta }$ Distribution for $\beta =6$
• Mutually avoiding paths in random media and largests eigenvalues of random matrices
• Asymptotics of the Tacnode process: a transition between the gap probabilities from the Tacnode to the Airy process
• Phase transition of the largest eigenvalue for non-null complex sample covariance matrices
• Airy Point Process via Supersymmetric Lifts
• The correspondence between Tracy-Widom (TW) and Adler-Shiota-van Moerbeke (ASvM) approaches in random matrix theory: the Gaussian case
• Edgeworth Expansion of the Largest Eigenvalue Distribution Function of GOE
• Limiting properties of random graph models with vertex and edge weights
• Cutoff profile of the Metropolis biased card shuffling
• Asymptotics of a discrete-time particle system near a reflecting boundary
• Tightness of discrete Gibbsian line ensembles
• Upper tail large deviations in Brownian directed percolation
• Random ballistic growth and diffusion in symmetric spaces
• Power law eigenvalue density, scaling and critical random matrix ensembles
• Log-gamma directed polymer with one free end via coordinate Bethe Ansatz
• Local semicircle law under moment conditions. Part II: Localization and delocalization
• On the Largest Eigenvalue of a Random Subgraph of the Hypercube
• Asymptotics for the Covariance of the Airy_2 process
• Non-intersecting path constructions for TASEP with inhomogeneous rates and the KPZ fixed point
• Performance of Statistical Tests for Single Source Detection using Random Matrix Theory
• An introduction to random matrix theory
• The KPZ equation and moments of random matrices
• Power countings versus physical scalings in disordered elastic systems - Case study of the one-dimensional interface
• Smoothed Analysis for the Conjugate Gradient Algorithm
• Universality for the Toda algorithm to compute the largest eigenvalue of a random matrix
• Weak detection in the spiked Wigner model
• Random polymers via orthogonal Whittaker and symplectic Schur functions
• Random Matrix Ensembles in Hyperchaotic Classical Dissipative Dynamical Systems
• The stochastic telegraph equation limit of the stochastic higher spin six vertex model
• Spectral Form Factor for Time-dependent Matrix model
• Non-probabilistic fermionic limit shapes
• On the deformed Pearcey determinant
• Large deviations of extreme eigenvalues of generalized sample covariance matrices
• Kernels for noninteracting fermions via a Green's function approach with applications to step potentials
• High dimensional regimes of non-stationary Gaussian correlated Wishart matrices
• Hole probability for noninteracting fermions in a $d$-dimensional trap
• Glass--like transition described by toppling of stability hierarchy
• Random walks and random permutations
• Recent Advances in Asymptotic Analysis
• Wigner meets 't Hooft near the black hole horizon
• The Airy${}_2$ process and the 3D Ising model
• Recursion Relation for Toeplitz Determinants and the Discrete Painlevé II Hierarchy
• Asymptotic expansions relating to the distribution of the length of longest increasing subsequences
• Jánossy densities and Darboux transformations for the Stark and cylindrical KdV equations
• Edgeworth Expansion of the Largest Eigenvalue Distribution Function of GUE Revisited
• From Maximum of Intervisit Times to Starving Random Walks
• A Unified Interface Model for Dissipative Transport of Bosons and Fermions
• Exact finite-size scaling for the random-matrix representation of bond percolation on square lattice
• Quantum Gravity Microstates from Fredholm Determinants
• Surface growth on treelike lattices and the upper critical dimension of the KPZ class
• The Asymptotic Distribution of Modularity in Weighted Signed Networks
• Stationary Higher Spin Six Vertex Model and $q$-Whittaker measure
• Universality of the double scaling limit in random matrix models
• Double scaling limit for matrix models with non analytic potentials
• Universality in Complex Wishart ensembles: The 2 cut case
• Empirical scaling of the length of the longest increasing subsequences of random walks
• Right large deviation principle for the top eigenvalue of the sum or product of invariant random matrices
• Correlation functions of the shifted Schur measure
• Dyson's non-intersecting Brownian motions with a few outliers
• Kardar-Parisi-Zhang growth on square domains that enlarge nonlinearly in time
• Asymptotics of the partition function of a random matrix model
• Fredholm determinant representation of the Painlevé II $\tau$-function
• Consecutive level spacings in the chiral Gaussian unitary ensemble: From the hard and soft edge to the bulk
• Singular asymptotics for solutions of the inhomogeneous Painlevé II equation
• Asymptotic behavior of the length of the longest increasing subsequences of random walks
• Fluctuations at the edges of the spectrum of the full rank deformed GUE
• Transversal fluctuations for increasing subsequences on the plane
• General truncated linear statistics for the top eigenvalues of random matrices
• Estimating Graph Dimension with Cross-validated Eigenvalues
• Discrete gap probabilities and discrete Painleve equations
• On the condition number of the critically-scaled Laguerre Unitary Ensemble
• Maximum-energy records in glassy energy landscapes
• Correlation Functions for a Chain of Short Range Oscillators
• Hopf algebra structure of generalized quasi-symmetric functions in partially commutative variables
• Scaling of Harmonic Oscillator Eigenfunctions and Their Nodal Sets Around the Caustic
• Linear processes in high-dimension: phase space and critical properties
• Local semicircle law at the spectral edge for Gaussian $\beta$-ensembles
• Limit distributions for KPZ growth models with spatially homogeneous random initial conditions
• Large deviation bounds for the Airy point process
• Limit Theory for the largest eigenvalues of sample covariance matrices with heavy-tails
• Resurgence of one-point functions in a matrix model for 2D type IIA superstrings
• Delay-Time and Thermopower Distributions at the Spectrum Edges of a Chaotic Scatterer
• The AKS Theorem, A.C.I. Systems and Random Matrix Theory
• Random matrices, log-gases and Holder regularity
• Nonequilibrium dynamics of noninteracting fermions in a trap
• Exclusion in Junction Geometries
• New edge asymptotics of skew Young diagrams via free boundaries
• Asymptotic expansions relating to the lengths of longest monotone subsequences of involutions
• Hankel operators that commute with second-order differential operators
• Increasing and Decreasing Subsequences of Permutations and Their Variants
• Random matrix theory and nested clustered portfolios on Mexican markets
• Zero temperature limit for (1+1) directed polymers with correlated random potential
• Multicritical random partitions
• Eigenvalues of Large Sample Covariance Matrices of Spiked Population Models
• Some conditional probabilities in the TASEP with second class particles
• Last Branching in Directed Last Passage Percolation
• Gas of baby universes in JT gravity and matrix models
• Hyperskewness of $(1+1)$-dimensional KPZ Height Fluctuations
• Tail States below the Thouless Gap in SNS junctions: Classical Fluctuations
• Tightness of Bernoulli Gibbsian line ensembles
• Non-commutative q-Painleve VI equation
• Comments on David Aldous and Persi Diaconis' "Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem"
• Fluctuations of the Longest Common Subsequence for Sequences of Independent Blocks
• Precise Deviations Results for the Maxima of Some Determinantal Point Processes: the Upper Tail
• Batch latency analysis and phase transitions for a tandem of queues with exponentially distributed service times
• Universal scaling and criticality of extremes in random matrix theory
• Peculiar spectral statistics of ensembles of trees and star-like graphs
• Initial perturbation matters: implications of geometry-dependent universal Kardar-Parisi-Zhang statistics for spatiotemporal chaos
• On the extreme value statistics of normal random matrices and 2D Coulomb gases: Universality and finite N corrections
• Painleve II in random matrix theory and related fields
• Integrable equations associated with the finite-temperature deformation of the discrete Bessel point process
• Spiking the random matrix hard edge
• A new commutativity property of exceptional orthogonal polynomials
• Two-point functions at arbitrary genus and its resurgence structure in a matrix model for 2D type IIA superstrings
• Hard edge for beta-ensembles and Painlevé III
• Random Circuits in the Black Hole Interior
• Interaction-correlated random matrices
• Location of Poles for the Hastings-McLeod Solution to the Second Painlevé Equation
• Emergent random matrix universality in quantum operator dynamics
• Asymptotics of the Airy-kernel determinant
• Point processes and the infinite symmetric group. Part VI: Summary of results
• A 2D Levy-flight model for the complex dynamics of real-life financial markets
• Extreme matrices or how an exponential map links classical and free extreme laws
• GUE $\times$ GUE limit law at hard shocks in ASEP
• Commuting integral and differential operators and the master symmetries of the Korteweg-de Vries equation
• Discrete and continuous Muttalib--Borodin processes I: the hard edge
• Constrained non-crossing Brownian motions, fermions and the Ferrari-Spohn distribution
• Edge Universality for Nonintersecting Brownian Bridges
• Muttalib--Borodin plane partitions and the hard edge of random matrix ensembles
• Random matrices in non-confining potentials
• Asymptotic Behaviours Given by Elliptic Functions in $P_I$--$P_V$
• On the combinatorics of last passage percolation in a quarter square and ${\mathrm{GOE}}^2$ fluctuations
• Limit shape and fluctuations for exactly solvable inhomogeneous corner growth models
• A Riemann Hilbert approach to the study of the generating function associated to the Pearcey process
• Overlap of a spherical spin glass model with microscopic external field
• Small deviations for beta ensembles
• All the lowest order PDE for spectral gaps of Gaussian matrices
• Uniqueness, mixing, and optimal tails for Brownian line ensembles with geometric area tilt
• A fully noncommutative Painlevé II hierarchy: Lax pair and solutions related to Fredholm determinants
• Universal Structure and Universal PDE for Unitary Ensembles
• Stochastic Growth in One Dimension and Gaussian Multi-Matrix Models
• Universality in unitary random matrix ensembles when the soft edge meets the hard edge
• Asymptotics of the Largest Eigenvalue Distribution of the Laguerre Unitary Ensemble
• Evaluation of integrals for the emptiness formation probability in the square-ice model
• Optimal tail estimates in $\beta$-ensembles and applications to last passage percolation
• Extreme-Value Statistics of Stochastic Transport Processes: Applications to Molecular Motors and Sports
• Clarkson-McLeod solutions of the fourth Painlevé equation and the parabolic cylinder-kernel determinant
• On Finite Rank Deformations of Wigner Matrices II: Delocalized Perturbations
• Universality in Complex Wishart ensembles: The 1 cut case
• The Eigenvalues of Random Matrices
• Interface Collisions
• A universality result for the smallest eigenvalues of certain sample covariance matrices
• Fast computation of the principal components of genotype matrices in Julia
• On the Limiting Shape of Young Tableaux Associated With Inhomogeneous Random Words
• Patience Sorting and Its Generalizations
• Asymptotic Independence in the Spectrum of the Gaussian Unitary Ensemble
• Eigenvalue variance bounds for Wigner and covariance random matrices
• Correlation function of the Schur process with a fixed final partition
• A Scaling Limit for t-Schur Measures
• Propagation of chaos for maxima of particle systems with mean-field drift interaction
• Central limit theorem for random partitions under the Plancherel measure
• On Spectral Norm of Large Band Random Matrices
• The Sigma Form for the PII Hierarchy
• The Tracy-Widom law for the Largest Eigenvalue of F Type Matrix
• Large gap asymptotics at the hard edge for product random matrices and Muttalib-Borodin ensembles
• Two-temperature statistics of free energies in (1+1) directed polymers
• Determinantal point processes from symplectic and orthogonal characters and applications
• Upper-tail large deviation principle for the ASEP
• Extremal Laws for Laplacian Random Matrices
• On ${\ell }_p$-Gaussian-Grothendieck problem
• Dimensional crossover in Kardar-Parisi-Zhang growth
• Domain-wall melting and entanglement in free-fermion chains with a band structure
• The Pascal Matrix, Commuting Tridiagonal Operators and Fourier Algebras
• Distribution of lowest eigenvalue in $k$-body bosonic random matrix ensembles
• Asymptotics of the deformed higher order Airy-kernel determinants and applications
• Finite-size relaxational dynamics of a spike random matrix spherical model
• The semiclassical limit of a quantum Zeno dynamics
• Universal Cusp Scaling in Random Partitions
• Integrable Differential Systems for Deformed Laguerre-Hahn Orthogonal Polynomials
• Coupling derivation of optimal-order central moment bounds in exponential last-passage percolation
• Stochastic and Quantum Dynamics of Repulsive Particles: from Random Matrix Theory to Trapped Fermions
• Gap probability for products of random matrices in the critical regime
• Asymptotic fluctuations of geometric q-TASEP, geometric q-PushTASEP and q-PushASEP
• On the scaling properties of (2+1) directed polymers in the high temperature limit
• Tracy-Widom distributions for the Gaussian orthogonal and symplectic ensembles revisited: a skew-orthogonal polynomials approach
• Global rigidity and exponential moments for soft and hard edge point processes
• Fluctuation Distributions of Energy Minima in Complex Landscapes
• Spectral rigidity of random Schrödinger operators via Feynman-Kac formulas
• Localization and free energy asymptotics in disordered statistical mechanics and random growth models
• Tracy-Widom limit for the largest eigenvalue of high-dimensional covariance matrices in elliptical distributions
• On the $q$-TASEP with a random initial condition
• Gap probability at the hard edge for random matrix ensembles with pole singularities in the potential
• Generic phase coexistence in the totally asymmetric kinetic Ising model
• A Limit Theorem for Stochastically Decaying Partitions at the Edge
• Two Lax systems for the Painlevé II equation, and two related kernels in random matrix theory
• Kernels and point processes associated with Whittaker functions
• Spectral Moments of Random Matrices with a Rank-One Pattern of Variances
• The asymptotic expansion of Tracy-Widom GUE law and symplectic invariants
• Aspects géométriques et intégrables des modèles de matrices aléatoires
• Extremal Eigenvalues and Eigenvectors of Deformed Wigner Matrices
• The tacnode Riemann-Hilbert problem
• Perturbed Laguerre Unitary Ensembles, Painlevé V and Information Theory
• Bessel process, Schramm-Loewner evolution, and Dyson model
• Longest increasing subsequence as expectation of a simple nonlinear stochastic PDE with a low noise intensity
• Diagonal Solutions to the 2-Toda Hierarchy
• Dissertation: Geodesics of Random Riemannian Metrics
• Jack deformations of Plancherel measures and traceless Gaussian random matrices
• Various equations for gap probabilities of coupled Gaussian matrices
• The probability density function tail of the Kardar-Parisi-Zhang equation in the strongly non-linear regime
• Limit theorems for a random directed slab graph
• Comportement asymptotique des polynômes orthogonaux associés à un poids ayant un zéro d'ordre fractionnaire sur le cercle. Applications aux valeurs propres d'une classe de matrices aléatoires unitaires
• Janossy densities for Unitary ensembles at the spectral edge
• Integrable operators and squares of Hankel Matrices
• Poisson convergence for the largest eigenvalues of Heavy Tailed Random Matrices
• Angular Synchronization by Eigenvectors and Semidefinite Programming
• Critical edge behavior in unitary random matrix ensembles and the thirty fourth Painleve transcendent
• The Distribution of the Largest Non-trivial Eigenvalues in Families of Random Regular Graphs
• Painlevé expressions for LOE, LSE and interpolating ensembles
• From Gumbel to Tracy-Widom
• Developments in Random Matrix Theory
• Optimal tail estimates for directed last passage site percolation with geometric random variables
• Extremal eigenvalue fluctuations in the GUE minor process and the law of fractional logarithm
• Linear systems and determinantal random point fields
• A PDE for the multi-time joint probability of the Airy process
• A System of Differential Equations for the Airy Process
• Concentration of the Spectral Measure for Large Random Matrices with Stable Entries
• A Card Shuffling Analysis of Deformations of the Plancherel Measure of the Symmetric Group
• Local Gaussian fluctuations in the Airy and discrete PNG processes
• Higher order analogues of the Tracy-Widom distribution and the Painleve II hierarchy
• On Painleve Related Functions Arising in Random Matrix Theory
• A unified matrix model including both CCA and F matrices in multivariate analysis: the largest eigenvalue and its applications
• The Length of the Longest Increasing Subsequence of a Random Mallows Permutation
• Simultaneous large deviations for the shape of Young diagrams associated with random words
• Boundary Conditions for Scaled Random Matrix Ensembles in the Bulk of the Spectrum
• Entropy method for the left tail
• The prolate spheroidal phenomena and bispectrality
• Hard and soft edge spacing distributions for random matrix ensembles with orthogonal and symplectic symmetry
• Universality for eigenvalue correlations from the modified Jacobi unitary ensemble
• Infrared self-consistent solutions of spinor QED3
• Convergence to the Tracy-Widom distribution for longest paths in a directed random graph
• Finite n Largest Eigenvalue Probability Distribution Function of Gaussian Ensembles
• Universality at the Edge for Unitary Matrix Models
• On the average of the Airy process and its time reversal
• Approximation of Rectangular Beta-Laguerre Ensembles and Large Deviations
• On the Modeling of Error Functions as High Dimensional Landscapes for Weight Initialization in Learning Networks
• An Overview of Geometric Asymptotic Analysis of Continuous and Discrete Painlevé Equations
• Gaussian fluctuations and moderate deviations of eigenvalues in unitary invariant ensembles
• Hirota bilinear approach to GUE, NLS, and Painlevé IV
• The largest eigenvalue distribution of the Laguerre unitary ensemble
• Correlation functions for random involutions
• Global Asymptotics of the Second Painlevé Equation in Okamoto's Space
• Exact solvability and asymptotic aspects of generalized XX0 spin chains
• Entanglement transitions induced by large deviations
• A novel Recurrence-Transience transition and Tracy-Widom growth in a cellular automaton with quenched noise
• Ordered spectral statistics in 1D disordered supersymmetric quantum mechanics and Sinai diffusion with dilute absorbers
• Quenched Central Limit Theorem in a Corner Growth Setting
• A growth model in a random environment
• Singular Value Statistics for the Spiked Elliptic Ginibre Ensemble
• On integrals of the tronquée solutions and the associated Hamiltonians for the Painlevé II equation
• Riemann-Hilbert Theory without local Parametrix Problems: Applications to Orthogonal Polynomials
• The Smallest Eigenvalue Distribution of the Jacobi Unitary Ensembles
• Eigenvector distribution in the critical regime of BBP transition
• On Asymptotic Expansions and Scales of Spectral Universality in Band Random Matrix Ensembles
• On the Evaluation of the Eigendecomposition of the Airy Integral Operator
• Peaks of cylindric plane partitions
• Invariance principle of random projection for the norm
• Poisson Statistics for the Largest Eigenvalues of Wigner Random Matrices with Heavy Tails
• Singular Value Perturbation and Deep Network Optimization
• Euclidean-to-Lorentzian wormhole transition and gravitational symmetry breaking in the Sachdev-Ye-Kitaev model
• Statistics of the non-zero eigenvalues and singular values of low-rank random matrices with non-negative entries
• On the Perturbed Second Painlevé Equation
• Vicious walkers, friendly walkers and Young tableaux III: Between two walls
• Computing the Tracy-Widom Distribution for Arbitrary $\beta >0$
• Deformed Fréchet law for Wigner and sample covariance matrices with tail in crossover regime
• The second class particle in the half-line open TASEP
• A convergence framework for Airy${}_{\beta }$ line ensemble via pole evolution
• $q$-deformation of random partitions, determinantal structure, and Riemann-Hilbert problem
• Longest increasing subsequences of random colored permutations
• Higher-Order Singular-Value Derivatives of Rectangular Real Matrices
• Universal scaling of higher-order cumulants in quantum isotropic spin chains
• Community-level Contagion among Diverse Financial Assets
• Pascal's Matrix, Point Counting on Elliptic Curves and Prolate Spheroidal Functions
• The Tracy-Widom distribution at large Dyson index
• Renormalization group for spectral collapse in random matrices with power-law variance profiles
• Geometry of the Ising persistence problem and the universal Bonnet-Manin Painlevé VI distribution
• Variations on Hammersley's interacting particle process
• Tightness of $(H,H^{RW})$-Gibbsian line ensembles
• The half-space Airy stat process
• Crossover in the log-gamma polymer from the replica coordinate Bethe Ansatz
• PhD thesis "Extreme value statistics of strongly correlated systems: fermions, random matrices and random walks"
• Critical edge behavior in the perturbed Laguerre ensemble and the Painleve V transcendent
• Operators associated with the soft and hard spectral edges of unitary ensembles
• Large deviations for the largest eigenvalue of rank one deformations of Gaussian ensembles
• Painleve IV asymptotics for orthogonal polynomials with respect to a modified Laguerre weight