Stochastic duality of ASEP with two particle types via symmetry of quantum groups of rank two

TL;DR

This paper explores two generalizations of the asymmetric simple exclusion process with two particle types, establishing self-duality and deriving explicit duality functions using quantum group symmetries, with applications to current moments.

Contribution

It introduces new duality results for multi-type ASEP models using quantum group symmetries, providing explicit duality functions and moment formulas.

Findings

Proved self-duality of the generalized ASEP models.

Derived explicit duality functions using quantum group symmetry.

Expressed moments of the exponentiated current in terms of multi-particle evolution.

Abstract

We study two generalizations of the asymmetric simple exclusion process with two types of particles. Particles of type 1 can jump over particles of type 2, while particles of type 2 can only influence the jump rates of particles of type 1. We prove that the processes are self-dual and explicitly write the duality function. As an application, an expression for the r-th moment of the exponentiated current is written in terms of r-particle evolution. The construction and proofs of duality are accomplished using symmetry of the quantum groups $U_q(\mathfrak{gl}_3)$ and $U_q(\mathfrak{sp}_4)$, with each node in the Dynkin diagram corresponding to a particle type, and the number of edges corresponding to the jump rates.