Introducing DASEP: the doubly asymmetric simple exclusion process

TL;DR

This paper introduces the DASEP, a new combinatorial model extending ASEP by allowing particles to change species, and explores its combinatorics, generating functions, and stationary probabilities.

Contribution

The paper presents the DASEP, a novel extension of ASEP that incorporates species-changing particles, with new combinatorial analysis and connections to existing ASEP results.

Findings

Derived the generating function for DASEP

Established relationships between DASEP and ASEP stationary probabilities

Explored combinatorial structures of DASEP on a one-dimensional lattice

Abstract

Research in combinatorics has often explored the asymmetric simple exclusion process (ASEP). The ASEP, inspired by examples from statistical mechanics, involves particles of various species moving around a lattice. With the traditional ASEP particles of a given species can move but do not change species. In this paper a new combinatorial formalism, the DASEP (doubly asymmetric simple exclusion process), is explored. The DASEP is inspired by biological processes where, unlike the ASEP, the particles can change from one species to another. The combinatorics of the DASEP on a one dimensional lattice are explored, including the associated generating function. The stationary probabilities of the DASEP are explored, and results are proven relating these stationary probabilities to those of the simpler ASEP.