Shape Fluctuations and Random Matrices

Abstract

We study a certain random groeth model in two dimensions closely related to the one-dimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the Tracy-Widom largest eigenvalue distribution for the Gaussian Unitary Ensemble.

Revised version. 51 pages

Cited by in corpus (491)

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• Replica Bethe ansatz derivation of the Tracy-Widom distribution of the free energy fluctuations in one-dimensional directed polymers
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• Facilitated Asymmetric Exclusion
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• The oriented swap process
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• Third-order phase transition in random tilings
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• Two-point free energy distribution function in (1+1) directed polymers
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• The free boundary Schur process and applications I
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• Determinantal transition kernels for some interacting particles on the line
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• Deformations of the Tracy-Widom distribution
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• Finite N corrections to the limiting distribution of the smallest eigenvalue of Wishart complex matrices
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• Attempted Bethe ansatz solution for one-dimensional directed polymers in random media
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• Crossover distributions at the edge of the rarefaction fan
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• TASEP on a ring in sub-relaxation time scale
• Kardar-Parisi-Zhang Universality of the Nagel-Schreckenberg Model
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• Microscopic concavity and fluctuation bounds in a class of deposition processes
• Static fluctuations of a thick 1D interface in the 1+1 Directed Polymer formulation
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• On the origins of scaling corrections in ballistic growth models
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• On integrable directed polymer models on the square lattice
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• Thermodynamics of the six-vertex model in an L-shaped domain
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• Mean field theory for skewed height profiles in KPZ growth processes
• Statistics of the maximal distance and momentum in a trapped Fermi gas at low temperature
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• The difference between two random mixed quantum states: exact and asymptotic spectral analysis
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• Random geometry and the Kardar-Parisi-Zhang universality class
• Scaling in the eigenvalue fluctuations of the empirical correlation matrices
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• Stationary half-space last passage percolation
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• Tail of the two-time height distribution for KPZ growth in one dimension
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• Accessing Kardar-Parisi-Zhang universality sub-classes with exciton polaritons
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• The 1+1 dimensional Kardar-Parisi-Zhang equation: more surprises
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• Gap statistics close to the quantile of a random walk
• Riemann surfaces for KPZ with periodic boundaries
• Determinant representation for some transition probabilities in the TASEP with second class particles
• Arctic curve of the free-fermion six-vertex model in an L-shaped domain
• Extreme boundary conditions and random tilings
• Eden model with nonlocal growth rules and the kinetic roughening in biological systems
• Exact Relaxation Dynamics in the Totally Asymmetric Simple Exclusion Process
• Non-intersecting Brownian bridges and the Laguerre Orthogonal Ensemble
• A Sublinear Variance Bound for Solutions of a Random Hamilton Jacobi Equation
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• Dynamical Correlations for Vicious Random Walk with a Wall
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• Optimal Exponent for Coalescence of Finite Geodesics in Exponential Last Passage Percolation
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• Average Characteristic Polynomials of Determinantal Point Processes
• Freezing transition of the directed polymer in a $1+d$ random medium : location of the critical temperature and unusual critical properties
• Spectrum of the totally asymmetric simple exclusion process on a periodic lattice - bulk eigenvalues
• Growth models, random matrices and Painleve transcendents
• Direct Evidence for Universal Statistics of Stationary Kardar-Parisi-Zhang Interfaces
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• Random walk generated by random permutations of {1,2,3, ..., n+1}
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• TASEP and generalizations: Method for exact solution
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• Log-Gamma directed polymer with fixed endpoints via the replica Bethe Ansatz
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• Multi-state asymmetric simple exclusion processes
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• Crossover between various initial conditions in KPZ growth: flat to stationary
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• Transition between characters of classical groups, decomposition of Gelfand-Tsetlin patterns and last passage percolation
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• Formulas for Joint Probabilities for the Asymmetric Simple Exclusion Process
• Superdiffusivity of two dimensional lattice gas models
• Random Transverse Field Ising Model in dimension $d=2,3$ : Infinite Disorder scaling via a non-linear transfer approach
• Non-equilibrium dynamics of polymers and interfaces in random media : conjecture $\psi =d_s/2$ for the barrier exponent
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• Tracy-Widom distribution as instanton sum of 2D IIA superstrings
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• Optimal-order exit point bounds in exponential last-passage percolation via the coupling technique
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• Formulas and Asymptotics for the Asymmetric Simple Exclusion Process
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• The Fluctuation-Dissipation Relations: Growth, Diffusion, and Beyond
• Unbounded Largest Eigenvalue of Large Sample Covariance Matrices: Asymptotics, Fluctuations and Applications
• Upper tail bounds for stationary KPZ models
• The Long ans Short Time Asymptotics of the Two-Time Distribution in Local Random Growth
• Statistics of TASEP with three merging characteristics
• Scaling limits for non-intersecting polymers and Whittaker measures
• Solution of the Kolmogorov equation for TASEP
• A new class of de Sitter vacua in String Theory Compactifications
• Height distributions in competitive one-dimensional Kardar-Parisi-Zhang systems
• Universal exit probabilities in the TASEP
• Emptiness formation probability of the six-vertex model and the sixth Painlevé equation
• Generalized Green Functions and current correlations in the TASEP
• Vicious Walkers and Hook Young Tableaux
• Limit shapes for inhomogeneous corner growth models with exponential and geometric weights
• Limiting current distribution for a two species asymmetric exclusion process
• Stochastic growth in time dependent environments
• Directed polymers and interfaces in random media : free-energy optimization via confinement in a wandering tube
• Midpoint distribution of directed polymers in the stationary regime: exact result through linear response
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• From Vicious Walkers to TASEP
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• Current fluctuations for totally asymmetric exclusion on the relaxation scale
• On the TASEP with Second Class Particles
• Transition probability and total crossing events in the multi-species asymmetric exclusion process
• Green functions for the TASEP with sublattice parallel update
• Random Hierarchical Matrices: Spectral Properties and Relation to Polymers on Disordered Trees
• Moderate deviation and exit time estimates for stationary Last Passage Percolation
• Mutually avoiding paths in random media and largests eigenvalues of random matrices
• How many longest increasing subsequences are there?
• Markov duality and Bethe ansatz formula for half-line open ASEP
• Arctic curves of the four-vertex model
• Multiline queues with spectral parameters
• Domain wall fluctuations of the six-vertex model at the ice point
• Decomposition of spectral density in individual eigenvalue contributions
• On the Variance of the Optimal Alignments Score for Binary Random Words and an Asymmetric Scoring Function
• Nonequilibrium transport and phase transitions in driven diffusion of interacting particles
• The KPZ fixed point for discrete time TASEPs
• Edge Statistics for Lozenge Tilings of Polygons, II: Airy Line Ensemble
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• Sample-to-sample fluctuations of transport coefficients in the totally asymmetric simple exclusion process with quenched disorder
• Remarks on the multi-species exclusion process with reflective boundaries
• Random ballistic growth and diffusion in symmetric spaces
• Transition Probabilities of the Bethe Ansatz Solvable Interacting Particle Systems
• Properties of the limit shape for some last passage growth models in random environments
• Matrix models and stochastic growth in Donaldson-Thomas theory
• Positive specializations of symmetric Grothendieck polynomials
• Radial Restricted Solid-on-Solid and Etching Interface Growth Models
• Limiting properties of random graph models with vertex and edge weights
• Interfacial depinning transitions in disordered media: revisiting an old puzzle
• A Unified Interface Model for Dissipative Transport of Bosons and Fermions
• Tracy-Widom asymptotics for a river delta model
• Volume of the set of LOCC-convertible quantum states
• The Einstein relation for the KPZ equation
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• Non-self-averaging of current in a totally asymmetric simple exclusion process with quenched disorder
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• The geometric Burge correspondence and the partition function of polymer replicas
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• Coarsening model on ${\mathbb{Z}}^d$ with biased zero-energy flips and an exponential large deviation bound for ASEP
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• Decorated Young Tableaux and the Poissonized Robinson-Schensted Process
• Current statistics in the q-boson zero range process
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• Singular asymptotics for solutions of the inhomogeneous Painlevé II equation
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• Current fluctuations of a system of one-dimensional random walks in random environment
• Crystal Growth Inside an Octant
• Importance Sampling for counting statistics in one-dimensional systems
• GOE and ${\mathrm{Airy}}_{2\to 1}$ marginal distribution via symplectic Schur functions
• Matrix Whittaker processes
• Width scaling of an interface constrained by a membrane
• Zero temperature limit for (1+1) directed polymers with correlated random potential
• Stochastic Dynamics of Growing Young Diagrams and Their Limit Shapes
• Last passage percolation and traveling fronts
• Exclusion in Junction Geometries
• Kardar-Parisi-Zhang growth on square domains that enlarge nonlinearly in time
• Random patterns generated by random permutations of natural numbers
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• From stability to chaos in last-passage percolation
• Directed polymers in random media under confining force
• Optimal tail estimates in $\beta$-ensembles and applications to last passage percolation
• Evaluation of integrals for the emptiness formation probability in the square-ice model
• Large deviations for the $q$-deformed polynuclear growth
• Parameter Permutation Symmetry in Particle Systems and Random Polymers
• A stationary model of non-intersecting directed polymers
• A fully noncommutative Painlevé II hierarchy: Lax pair and solutions related to Fredholm determinants
• Passive Tracer Dynamics in Slow-Bond Problem
• Correlation function of the Schur process with a fixed final partition
• Generalized Laguerre Unitary Ensembles and an interacting particles model with a wall
• Dimensional crossover in Kardar-Parisi-Zhang growth
• Longest increasing subsequence as expectation of a simple nonlinear stochastic PDE with a low noise intensity
• Coupling derivation of optimal-order central moment bounds in exponential last-passage percolation
• On the $q$-TASEP with a random initial condition
• Last passage percolation and limit theorems in Barak-Erdős directed random graphs and related models
• Two-time distribution functions in the Gaussian model of randomly forced Burgers turbulence
• Two-temperature statistics of free energies in (1+1) directed polymers
• TASEP with a general initial condition and a deterministically moving wall
• On the scaling properties of (2+1) directed polymers in the high temperature limit
• Directed polymer in a random medium of dimension 1+1 and 1+3: weights statistics in the low-temperature phase
• Generic phase coexistence in the totally asymmetric kinetic Ising model
• Sparse Recovery from Extreme Eigenvalues Deviation Inequalities
• The Tracy-Widom distribution at large Dyson index
• Longest weakly increasing subsequences of discrete random walks on the integers with heavy tailed distribution of increments
• On the duality between particles and polymers
• Geodesic trees in last passage percolation and some related problems
• Simultaneous large deviations for the shape of Young diagrams associated with random words
• The Epstein-Glaser approach to pQFT: graphs and Hopf algebras
• A convergence framework for Airy${}_{\beta }$ line ensemble via pole evolution
• Stabilization Time for a Type of Evolution on Binary Strings
• Ordered spectral statistics in 1D disordered supersymmetric quantum mechanics and Sinai diffusion with dilute absorbers
• Discrete Whittaker processes
• Free fermionic probability theory and K-theoretic Schubert calculus
• Point Fields of Last Passage Percolation and Coalescing Fractional Brownian Motions
• Non-normal limiting distribution for optimal alignment scores of strings in binary alphabets
• Non symmetric Cauchy kernel, crystals and last passage percolation