Formulas and Asymptotics for the Asymmetric Simple Exclusion Process

TL;DR

This paper reviews and synthesizes key results on the asymmetric simple exclusion process (ASEP), including exact formulas, Fredholm determinants, and asymptotic behavior, to establish connections with KPZ universality.

Contribution

It provides an integrated overview of recent advances in ASEP analysis, highlighting formulas, representations, and asymptotics that deepen understanding of KPZ universality.

Findings

Exact formulas for configuration probabilities in ASEP

Fredholm determinant representations of ASEP solutions

Asymptotic results confirming KPZ universality

Abstract

This is an expanded version of a series of lectures delivered by the second author in June, 2009. It describes the results of three of the authors' papers on ASEP, from the derivation of exact formulas for configuration probabilities, through Fredholm determinant representation, to asymptotics for ASEP with step initial condition establishing KPZ universality. Although complete proofs are in general not given, at least the main elements of them are.