Asymmetric Simple Exclusion Process and Modified Random Matrix Ensembles

TL;DR

This paper explores the fluctuation behavior of ASEP on an infinite lattice, extending known results to new initial conditions and revealing a phase transition in current fluctuations.

Contribution

It introduces modified random matrix ensembles corresponding to general ASEP initial conditions and analyzes the resulting phase change in fluctuation behavior.

Findings

Derived new random matrix ensembles for ASEP initial conditions

Identified a phase transition in current fluctuation at a critical position

Extended Johansson's formula to broader initial conditions

Abstract

We study the fluctuation properties of the asymmetric simple exclusion process (ASEP) on an infinite one-dimensional lattice. When $N$ particles are initially situated in the negative region with a uniform density $\rho_-=1$, Johansson showed the equivalence of the current fluctuation of ASEP and the largest eigenvalue distribution of random matrices. We extend Johansson's formula and derive modified ensembles of random matrices, corresponding to general ASEP initial conditions. Taking the scaling limit, we find that a phase change of the asymptotic current fluctuation occurs at a critical position.