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

References in corpus (8)

• Exact scaling functions for one-dimensional stationary KPZ growth
• Fluctuation properties of the TASEP with periodic initial configuration
• 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
• Fluctuations of a one-dimensional polynuclear growth model in a half space
• Determinant solution for the Totally Asymmetric Exclusion Process with parallel update
• Polynuclear growth model, GOE${}^2$ and random matrix with deterministic source

Cited by in corpus (5)

• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries
• Cumulants of the current in the weakly asymmetric exclusion process
• Fluctuations and skewness of the current in the partially asymmetric exclusion process
• A combinatorial solution for the current fluctuations in the exclusion process