The inhomogeneous multispecies PushTASEP: Dynamics and symmetry

TL;DR

This paper introduces a multispecies inhomogeneous PushTASEP on a finite ring, characterizes its stationary distribution using ASEP polynomials, and explores its symmetry properties and correlation formulas.

Contribution

It constructs a multiline process for the multispecies PushTASEP, identifies its stationary distribution via ASEP polynomials, and analyzes symmetry and correlation structures.

Findings

Stationary distribution proportional to ASEP polynomials at q=1, t=0

Symmetry properties under rate interchange for both equilibrium and non-equilibrium

Explicit formulas for two-point correlations using Schur functions

Abstract

We introduce and study a natural multispecies variant of the inhomogeneous PushTASEP with site-dependent rates on the finite ring. We show that the stationary distribution of this process is proportional to the ASEP polynomials at $q = 1$ and $t = 0$. This is done by constructing a multiline process which projects to the multispecies PushTASEP, and identifying its stationary distribution using time-reversal arguments. We also study symmetry properties of the process under interchange of the rates associated to the sites. These results hold not just for events depending on the configuration at a single time in equilibrium, but also for systems out of equilibrium and for events depending on the path of the process over time. Lastly, we give explicit formulas for nearest-neighbour two-point correlations in terms of Schur functions.