Stationary Distribution of open Asymmetric Simple Exclusion Processes on an Interval as a marginal of a two-layer ensemble

TL;DR

This paper derives a new representation for the stationary distribution of open ASEP on an interval as a marginal of a two-layer ensemble, extending previous results to broader regions.

Contribution

It introduces a novel representation of ASEP's stationary distribution as a marginal of a two-layer ensemble, valid in fan and shock regions.

Findings

Representation valid in fan and shock regions

Extension of previous ASEP representations

Provides recursion for two-layer weight function

Abstract

We investigate the asymmetric simple exclusion process (ASEP) on an interval with open boundaries. We provide a representation for its stationary distribution as a marginal of the top layer of a two-layer ensemble under Liggett's condition. The representation is valid in the fan region and in the shock region, extending the representation previously obtained in [Bryc-Zatitskii-2024 arXiv:2403.03275] to ASEP. We also give a recursion for the two-layer weight function.