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

TL;DR

This paper reviews how random matrix theory techniques are applied to analyze fluctuations in the one-dimensional asymmetric exclusion process, connecting it to the KPZ universality class and growth models.

Contribution

It introduces the application of random matrix methods to the asymmetric simple exclusion process and elucidates their connection to growth models and fluctuation analysis.

Findings

Random matrix techniques effectively analyze fluctuations in ASEP.

Connections established between ASEP, polynuclear growth models, and Green's function methods.

Provides a comprehensive review of fluctuation analysis in KPZ universality class.

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.