The combinatorics of hopping particles and positivity in Markov chains
Combinatorics
2022-02-02 v1 Mathematical Physics
math.MP
Probability
Abstract
The asymmetric simple exclusion process (ASEP) is a model for translation in protein synthesis and traffic flow; it can be defined as a Markov chain describing particles hopping on a one-dimensional lattice. In this article I give an overview of some of the connections of the stationary distribution of the ASEP to combinatorics (tableaux and multiline queues) and special functions (Askey-Wilson polynomials, Macdonald polynomials, and Schubert polynomials). I also make some general observations about positivity in Markov chains.
Keywords
Cite
@article{arxiv.2202.00214,
title = {The combinatorics of hopping particles and positivity in Markov chains},
author = {Lauren K. Williams},
journal= {arXiv preprint arXiv:2202.00214},
year = {2022}
}
Comments
16 pages, 10 figures, 6 tables