An Inhomogeneous Multispecies TASEP on a Ring

TL;DR

This paper studies a multispecies exclusion process on a ring, generalizing existing conjectures and introducing new processes to analyze stationary distributions, with progress on special cases and new proof techniques.

Contribution

It generalizes conjectures about multispecies TASEP on a ring, proves them in special cases, and introduces a new process with minimality properties for multiline queues.

Findings

Proved conjectures for two special cases with generalized rates.

Defined a new multiline queue process with minimality properties.

Provided an alternative proof for the three-species case with arbitrary jump rates.

Abstract

We reinterpret and generalize conjectures of Lam and Williams as statements about the stationary distribution of a multispecies exclusion process on the ring. The central objects in our study are the multiline queues of Ferrari and Martin. We make some progress on some of the conjectures in different directions. First, we prove their conjectures in two special cases by generalizing the rates of the Ferrari-Martin transitions. Secondly, we define a new process on multiline queues, which have a certain minimality property. This gives another proof for one of the special cases; namely arbitrary jump rates for three species.