Matrix product solution to an inhomogeneous multi-species TASEP

TL;DR

This paper introduces a matrix product approach to analyze the stationary state of an inhomogeneous multi-species TASEP, connecting it to affine braid arrangements and graphical constructions, advancing understanding of complex exclusion processes.

Contribution

It provides a novel matrix product representation for the stationary state of an inhomogeneous multi-species TASEP, linking algebraic and graphical methods.

Findings

Matrix product representation for the stationary state.

Equivalence to a graphical construction by Ayyer and Linusson.

Connection to a Markov chain on the symmetric group.

Abstract

We study a multi-species exclusion process with inhomogeneous hopping rates. This model is equivalent to a Markov chain on the symmetric group that corresponds to a random walk in the affine braid arrangement. We find a matrix product representation for the stationary state of this model. We also show that it is equivalent to a graphical construction proposed by Ayyer and Linusson, which generalizes Ferrari and Martin's construction.