On ASEP with Step Bernoulli Initial Condition

TL;DR

This paper extends ASEP analysis to step Bernoulli initial conditions, providing a Fredholm determinant representation and asymptotic results that confirm KPZ universality for particle position and current fluctuations.

Contribution

It introduces a Fredholm determinant formula for ASEP with step Bernoulli initial condition and establishes KPZ universality in this setting.

Findings

Fredholm determinant representation of particle position distribution

Asymptotic analysis confirming KPZ universality

Results applicable to current fluctuation statistics

Abstract

This paper extends results of earlier work on ASEP to the case of step Bernoulli initial condition. The main results are a representation in terms of a Fredholm determinant for the probability distribution of a fixed particle, and asymptotic results which in particular establish KPZ universality for this probability in one regime. (And, as a corollary, for the current fluctuations.)