Asymptotics in ASEP with Step Initial Condition

TL;DR

This paper derives asymptotic distributions for particle positions in ASEP with step initial condition, revealing a new distribution and extending Johansson's results from TASEP to ASEP.

Contribution

It introduces three asymptotic results for ASEP particle positions, including a new distribution function and an extension of Johansson's TASEP findings to ASEP.

Findings

A new distribution function for ASEP particle positions

Extension of Johansson's TASEP results to ASEP

Asymptotic formulas involving Fredholm determinants

Abstract

In previous work the authors considered the asymmetric simple exclusion process on the integer lattice in the case of step initial condition, particles beginning at the positive integers. There it was shown that the probability distribution for the position of an individual particle is given by an integral whose integrand involves a Fredholm determinant. Here we use this formula to obtain three asymptotic results for the positions of these particles. In one an apparently new distribution function arises and in another the distribuion function F_2 arises. The latter extends a result of Johansson on TASEP to ASEP.