The Stationary Measure of a 2-type Totally Asymmetric Exclusion Process

TL;DR

This paper provides a combinatorial description of the stationary measure for a 2-type TASEP, revealing underlying structures and connecting uniform measures on larger state spaces to the stationary distribution.

Contribution

It introduces a novel combinatorial framework for understanding the stationary measure of a 2-type TASEP on Z and Z_N, linking it to uniform measures on extended state spaces.

Findings

Describes the stationary measure via combinatorial operations.

Connects the measure to uniform distributions on larger state spaces.

Unveils structural insights into TASEP with second class particles.

Abstract

We give a combinatorial description of the stationary measure for a totally asymmetric exclusion process (TASEP) with second class particles, on either Z or on the cycle Z_N. The measure is the image by a simple operation of the uniform measure on some larger finite state space. This reveals a combinatorial structure at work behind several results on the TASEP with second class particles.