Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques

Abstract

The studies of fluctuations of the one-dimensional Kardar-Parisi-Zhang universality class using the techniques from random matrix theory are reviewed from the point of view of the asymmetric simple exclusion process. We explain the basics of random matrix techniques, the connections to the polynuclear growth models and a method using the Green's function.

41 pages, 10 figures, minor corrections, references added

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Cited by in corpus (54)

• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• A pedestrian's view on interacting particle systems, KPZ universality, and random matrices
• Full counting statistics in a propagating quantum front and random matrix spectra
• Exact Current Statistics of the ASEP with Open Boundaries
• Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition
• The Exclusion Process: A paradigm for non-equilibrium behaviour
• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Stationary correlations for the 1D KPZ equation
• Large time asymptotics of growth models on space-like paths II: PNG and parallel TASEP
• An Exact Formula for the Statistics of the Current in the TASEP with Open Boundaries
• Last Passage Percolation with a Defect Line and the Solution of the Slow Bond Problem
• Some Exact Results for the Exclusion Process
• Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries
• Signatures of critical full counting statistics in a quantum-dot chain
• Superdiffusivity of the 1D lattice Kardar-Parisi-Zhang equation
• Current fluctuations for TASEP: A proof of the Prähofer--Spohn conjecture
• Current moments of 1D ASEP by duality
• Twenty five years after KLS: A celebration of non-equilibrium statistical mechanics
• Cumulants of the current in the weakly asymmetric exclusion process
• Two speed TASEP
• Tree structures for the current fluctuations in the exclusion process
• Matrix Ansatz for the Fluctuations of the Current in the ASEP with Open Boundaries
• Replica approach to the KPZ equation with half Brownian motion initial condition
• Fluctuations and skewness of the current in the partially asymmetric exclusion process
• Matrix model from N = 2 orbifold partition function
• Kardar-Parisi-Zhang Universality of the Nagel-Schreckenberg Model
• Spectrum of the totally asymmetric simple exclusion process on a periodic lattice -- first excited states
• Replica Bethe Ansatz solution to the Kardar-Parisi-Zhang equation on the half-line
• Delta-Bose gas on a half-line and the KPZ equation: boundary bound states and unbinding transitions
• Determinant representation for some transition probabilities in the TASEP with second class particles
• When fast and slow interfaces grow together: connection to the half-space problem of the Kardar-Parisi-Zhang class
• Spectrum of the totally asymmetric simple exclusion process on a periodic lattice - bulk eigenvalues
• Compact Waves in Microscopic Nonlinear Diffusion
• Circular Kardar-Parisi-Zhang interfaces evolving out of the plane
• Invariant Measures for TASEP with a Slow Bond
• Current fluctuations and large deviations for periodic TASEP on the relaxation scale
• Multi-state asymmetric simple exclusion processes
• Perturbative solution for the spectral gap of the weakly asymmetric exclusion process
• Brownian bridges for late time asymptotics of KPZ fluctuations in finite volume
• Melting of an Ising Quadrant
• KPZ universality class and the anchored Toom interface
• Finite GUE distribution with cut-off at a shock
• Exact Large Deviations of the Current in the Asymmetric Simple Exclusion Process with Open Boundaries
• Green functions for the TASEP with sublattice parallel update
• KPZ fluctuations in finite volume
• Limit distributions for KPZ growth models with spatially homogeneous random initial conditions
• Stochastic Dynamics of Growing Young Diagrams and Their Limit Shapes
• Zone clearance in an infinite TASEP with a step initial condition
• From the Riemann surface of TASEP to ASEP
• A combinatorial solution for the current fluctuations in the exclusion process
• Relaxation dynamics of closed diffusive systems with infinitesimal Langmuir kinetics
• Dimers and orthogonal polynomials: connections with random matrices
• Veneziano Amplitudes, Spin Chains and String Models
• Stochastic and Quantum Dynamics of Repulsive Particles: from Random Matrix Theory to Trapped Fermions