Matrix representation of the stationary measure for the multispecies TASEP

TL;DR

This paper develops a matrix product approach to describe the stationary distribution of the multispecies TASEP, linking it to queueing theory and algebraic structures, and provides an algebraic proof for the case of three species.

Contribution

It introduces a matrix representation for the stationary measure of multispecies TASEP, connecting it with queueing theory and quadratic algebra structures, and offers an algebraic proof for three species.

Findings

Matrix product formulation for N species TASEP stationary measure

Connection established between matrix approach and queueing theory

Algebraic proof provided for the case of three species

Abstract

In this work we construct the stationary measure of the N species totally asymmetric simple exclusion process in a matrix product formulation. We make the connection between the matrix product formulation and the queueing theory picture of Ferrari and Martin. In particular, in the standard representation, the matrices act on the space of queue lengths. For N >2 the matrices in fact become tensor products of elements of quadratic algebras. This enables us to give a purely algebraic proof of the stationary measure which we present for N =3.