The combinatorics of hopping particles and positivity in Markov chains
Autor: | Williams, Lauren K. |
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Rok vydání: | 2022 |
Předmět: | |
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 |
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