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Paper detail

The combinatorics of hopping particles and positivity in Markov chains

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.

preprint2022arXivOpen access
Lauren K. Williams
math.COmath-phmath.PRmath.MP
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Lauren K. Williams

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