The combinatorics of hopping particles and positivity in Markov chains

Autor:	Williams, Lauren K.
Rok vydání:	2022
Předmět:	Mathematics - Combinatorics Mathematical Physics Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	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. Comment: 16 pages, 10 figures, 6 tables
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2202.00214 Zobrazit plný text záznamu View this record from Arxiv