Coxeter Group Actions on Interacting Particle Systems

TL;DR

This paper demonstrates how Coxeter group actions explain the color-position symmetry in colored ASEP and related systems, providing new insights into their structure and particle position asymptotics.

Contribution

It introduces a conceptual proof linking Coxeter group actions to symmetry properties in interacting particle systems, extending to generalized ASEP models.

Findings

Color-position symmetry explained via Coxeter groups

Asymptotic behavior of second-class particles derived

Applicable to systems with open boundaries and generalized parameters

Abstract

We provide a conceptual proof of the color-position symmetry of colored ASEP by relating it to the actions of Coxeter groups. The group action (and hence the color-position symmetry) also applies to more general interacting particle systems, such as the colored ASEP(q,j) or systems with open boundary conditions. As an application, we find the asymptotics of the expected positions of second-class particles in the ASEP(q,j).