Spatial correlations of the 1D KPZ surface on a flat substrate

Abstract

We study the spatial correlations of the one-dimensional KPZ surface for the flat initial condition. It is shown that the multi-point joint distribution for the height is given by a Fredholm determinant, with its kernel in the scaling limit explicitly obtained. This may also describe the dynamics of the largest eigenvalue in the GOE Dyson's Brownian motion model. Our analysis is based on a reformulation of the determinantal Green's function for the totally ASEP in terms of a vicious walk problem.

11 pages, 2 figures

References in corpus (14)

• Shape Fluctuations and Random Matrices
• On Orthogonal and Symplectic Matrix Ensembles
• Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
• Discrete polynuclear growth and determinantal processes
• Exact Large Deviation Function in the Asymmetric Exclusion Process
• Exact scaling functions for one-dimensional stationary KPZ growth
• Exact Solution of the Master Equation for the Asymmetric Exclusion Process
• Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems
• Fluctuations of the one-dimensional polynuclear growth model with external sources
• Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process
• Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues
• Differential Equations for Dyson Processes
• Fluctuations of a one-dimensional polynuclear growth model in a half space
• Asymmetric Simple Exclusion Process and Modified Random Matrix Ensembles

Cited by in corpus (128)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Fluctuation properties of the TASEP with periodic initial configuration
• An exact solution for the KPZ equation with flat initial conditions
• The one-dimensional KPZ equation and its universality class
• A pedestrian's view on interacting particle systems, KPZ universality, and random matrices
• Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process
• An appetizer to modern developments on the Kardar-Parisi-Zhang universality class
• Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
• Integral Formulas for the Asymmetric Simple Exclusion Process
• Anisotropic growth of random surfaces in 2+1 dimensions
• Logarithmic current fluctuations in non-equilibrium quantum spin chains
• Non-perturbative renormalisation group for the Kardar-Parisi-Zhang equation: general framework and first applications
• Transition between Airy_1 and Airy_2 processes and TASEP fluctuations
• Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals
• Stationary correlations for the 1D KPZ equation
• Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques
• Extremely large scale simulation of a Kardar-Parisi-Zhang model using graphics cards
• A determinantal formula for the GOE Tracy-Widom distribution
• Large time asymptotics of growth models on space-like paths II: PNG and parallel TASEP
• On integrability of zero-range chipping models with factorized steady state
• Nonperturbative renormalization group for the stationary Kardar-Parisi-Zhang equation: scaling functions and amplitude ratios in 1+1, 2+1 and 3+1 dimensions
• Kardar-Parisi-Zhang universality class in 2+1 dimensions: Universal geometry-dependent distributions and finite-time corrections
• Airy processes and variational problems
• Crossover from Growing to Stationary Interfaces in the Kardar-Parisi-Zhang Class
• Continuum statistics of the Airy2 process
• Local behavior and hitting probabilities of the Airy1 process
• Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition
• Free fermions in disguise
• Slow decorrelations in KPZ growth
• Finite time corrections in KPZ growth models
• Exponents governing the rarity of disjoint polymers in Brownian last passage percolation
• From interacting particle systems to random matrices
• Finite-time fluctuations for the totally asymmetric exclusion process
• Family-Vicsek Scaling of Roughness Growth in a Strongly Interacting Bose Gas
• Endpoint distribution of directed polymers in 1+1 dimensions
• Universal fluctuations in KPZ growth on one-dimensional flat substrates
• The Airy_1 process is not the limit of the largest eigenvalue in GOE matrix diffusion
• On Time Correlations for KPZ Growth in One Dimension
• Determinant solution for the Totally Asymmetric Exclusion Process with parallel update
• The Kardar-Parisi-Zhang equation with spatially correlated noise: a unified picture from nonperturbative renormalization group
• Two speed TASEP
• Universality and dependence on initial conditions in the class of the nonlinear molecular beam epitaxy equation
• Slow relaxation and aging kinetics for the driven lattice gas
• A Pfaffian representation for flat ASEP
• Exact confirmation of 1D nonlinear fluctuating hydrodynamics for a two-species exclusion process
• Time-time covariance for last passage percolation with generic initial profile
• Interface fluctuations for deposition on enlarging flat substrates
• Scaling limit for Brownian motions with one-sided collisions
• Anomalous shock fluctuations in TASEP and last passage percolation models
• Tracy-Widom asymptotics for q-TASEP
• Initial pseudo-steady state & asymptotic KPZ universality in semiconductor on polymer deposition
• Transversal fluctuations of the ASEP, stochastic six vertex model, and Hall-Littlewood Gibbsian line ensembles
• Anisotropic KPZ growth in 2+1 dimensions: fluctuations and covariance structure
• Replica approach to the KPZ equation with half Brownian motion initial condition
• Kardar-Parisi-Zhang Interfaces with Inward Growth
• Determinant solution for the Totally Asymmetric Exclusion Process with parallel update II. Ring geometry
• TASEP on a ring in sub-relaxation time scale
• One-sided reflected Brownian motions and the KPZ fixed point
• Determinantal structures in the O'Connell-Yor directed random polymer model
• How flat is flat in random interface growth?
• From Painlevé to Zakharov-Shabat and beyond: Fredholm determinants and integro-differential hierarchies
• Crossover from droplet to flat initial conditions in the KPZ equation from the replica Bethe ansatz
• Stationary half-space last passage percolation
• Emergence of jams in the generalized totally asymmetric simple exclusion process
• Delta-Bose gas on a half-line and the KPZ equation: boundary bound states and unbinding transitions
• Accessing Kardar-Parisi-Zhang universality sub-classes with exciton polaritons
• KP governs random growth off a one dimensional substrate
• The 1+1 dimensional Kardar-Parisi-Zhang equation: more surprises
• Riemann surfaces for KPZ with periodic boundaries
• Geometry dependence in linear interface growth
• Determinant representation for some transition probabilities in the TASEP with second class particles
• Strong-coupling phases of the anisotropic Kardar-Parisi-Zhang equation
• Kardar-Parisi-Zhang growth on one-dimensional decreasing substrates
• When fast and slow interfaces grow together: connection to the half-space problem of the Kardar-Parisi-Zhang class
• Ballistic deposition patterns beneath a growing KPZ interface
• Multiplicative functionals on ensembles of non-intersecting paths
• Non-intersecting Brownian bridges and the Laguerre Orthogonal Ensemble
• Tails of the endpoint distribution of directed polymers
• TASEP and generalizations: Method for exact solution
• Kardar-Parisi-Zhang Interfaces with Curved Initial Shapes and Variational Formula
• Supremum of the Airy2 process minus a parabola on a half line
• Circular Kardar-Parisi-Zhang interfaces evolving out of the plane
• Relationships between $\tau$-function and Fredholm determinant expressions for gap probabilities in random matrix theory
• A limit theorem at the spectral edge for corners of time-dependent Wigner matrices
• Partial yet definite emergence of the Kardar-Parisi-Zhang class in isotropic spin chains
• Shock fluctuations in flat TASEP under critical scaling
• Exact Formulas of the Transition Probabilities of the Multi-Species Asymmetric Simple Exclusion Process
• Multi-state asymmetric simple exclusion processes
• Distribution of a particle's position in the ASEP with the {alternating} initial condition
• Current fluctuations and large deviations for periodic TASEP on the relaxation scale
• On the partial connection between random matrices and interacting particle systems
• Tracy-Widom limit of q-Hahn TASEP
• Crossover between various initial conditions in KPZ growth: flat to stationary
• The asymmetric simple exclusion process on chains with a shortcut revisited
• Transition between characters of classical groups, decomposition of Gelfand-Tsetlin patterns and last passage percolation
• Riemann surface for TASEP with periodic boundaries
• The current distribution of the multiparticle hopping asymmetric diffusion model
• Universal exit probabilities in the TASEP
• Solution of the Kolmogorov equation for TASEP
• Limiting current distribution for a two species asymmetric exclusion process
• Generalized Green Functions and current correlations in the TASEP
• Width and extremal height distributions of fluctuating interfaces with window boundary conditions
• Airy process with wanderers, KPZ fluctuations, and a deformation of the Tracy--Widom GOE distribution
• Green functions for the TASEP with sublattice parallel update
• KPZ fluctuations in finite volume
• One-dimensional irreversible aggregation with TASEP dynamics
• From Vicious Walkers to TASEP
• Transition probability and total crossing events in the multi-species asymmetric exclusion process
• Tail decay for the distribution of the endpoint of a directed polymer
• Transition Probabilities of the Bethe Ansatz Solvable Interacting Particle Systems
• On the exponent governing the correlation decay of the Airy${}_1$ process
• Non-intersecting path constructions for TASEP with inhomogeneous rates and the KPZ fixed point
• The KPZ fixed point for discrete time TASEPs
• TASEP fluctuations with soft-shock initial data
• Current statistics in the q-boson zero range process
• Kardar-Parisi-Zhang growth on square domains that enlarge nonlinearly in time
• GOE and ${\mathrm{Airy}}_{2\to 1}$ marginal distribution via symplectic Schur functions
• Exact solution of interacting particle systems related to random matrices
• On the spatial persistence for Airy processes
• Passive Tracer Dynamics in Slow-Bond Problem
• On ASEP with Periodic Step Bernoulli Initial Condition
• Nonstationary generalized TASEP in KPZ and jamming regimes
• One-point height fluctuations and two-point correlators of $(2+1)$ cylindrical KPZ systems
• Asymptotic fluctuations of geometric q-TASEP, geometric q-PushTASEP and q-PushASEP
• TASEP with a general initial condition and a deterministically moving wall
• The oriented swap process and last passage percolation
• On the duality between particles and polymers
• A convergence framework for Airy${}_{\beta }$ line ensemble via pole evolution