Séminaire Lotharingien de Combinatoire, 91B.55 (2024), 12 pp.
Yuhan Jiang
The Doubly Asymmetric Simple Exclusion Process, The Colored Boolean Process, and The Restricted Random Growth Model
Abstract.
The multispecies asymmetric simple exclusion process (mASEP) is a Markov chain in which particles of different species hop along a one-dimensional lattice.
This paper studies the doubly asymmetric simple exclusion process
DASEP(n,p,q) in which q particles with
species 1,...,p hop
along a circular lattice with n sites, but also the particles are
allowed to spontaneously change from one species to another.
In this paper, we introduce two related Markov chains called the
colored Boolean process and the restricted random growth model, and we
show that the DASEP lumps to the colored Boolean process, and the
colored Boolean process lumps to the restricted random growth model.
This allows us to generalize a theorem of David Ash on the relations
between sums of steady state probabilities.
We also give explicit formulas for the stationary distribution of
DASEP(n,2,2).
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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