Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries

TL;DR

This paper demonstrates that the normalization of the stationary state in a multi-species asymmetric exclusion process is a special case of Koornwinder polynomials, revealing a factorization property related to two-species ASEP.

Contribution

It establishes a novel connection between multi-species ASEP stationary states and Koornwinder polynomials, providing a new algebraic perspective.

Findings

Normalization of mASEP is a Koornwinder polynomial specialization

Normalisation factorizes into products over two-species ASEP

Provides algebraic insight into multi-species exclusion processes

Abstract

We prove that the normalisation of the stationary state of the multi-species asymmetric simple exclusion process (mASEP) is a specialisation of a Koornwinder polynomial. As a corollary we obtain that the normalisation of mASEP factorises as a product over multiple copies of the two-species ASEP.