Introducing DASEP: the doubly asymmetric simple exclusion process
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.
Received: December 31, 2021.
Revised: October 19, 2022.
Published: August 31, 2023.
