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Interacting particle systems and random walks on Hecke algebras

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arxiv 2003.02730 v1 pith:WIDM6JDT submitted 2020-03-05 math.PR math-phmath.MP

Alexey Bufetov This is my paper · ORCID
classification math.PRmath-phmath.MP
keywords systemsalgebrasasepclassheckeinteractingparticlerandom
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In this paper we show that a variety of interacting particle systems with multiple species can be viewed as random walks on Hecke algebras. This class of systems includes the asymmetric simple exclusion process (ASEP), M-exclusion TASEP, ASEP(q,j), stochastic vertex models, and many others. As an application, we study the asymptotic behavior of second class particles in some of these systems.

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