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Schubert polynomials, the inhomogeneous TASEP, and evil-avoiding permutations

[HYBRID WORKSHOP] Connections and Introductory Workshop: Universality and Integrability in Random Matrix Theory and Interacting Particle Systems, Part 1 August 23, 2021 - August 27, 2021

August 23, 2021 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Lauren Williams (Harvard University)
Location: MSRI: Simons Auditorium, Online/Virtual
Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Schubert Polynomials, The Inhomogeneous TASEP, And Evil-Avoiding Permutations

Abstract

The totally asymmetric simple exclusion process (TASEP) was introduced around 1970 as a model for translation in protein synthesis and traffic flow. The inhomogeneous TASEP is a Markov chain of weighted particles hopping on a lattice, in which the hopping rate depends on the weight of the particles being interchanged. We will consider the case where the lattice is a ring, and each particle has a distinct weight, so that we can think of this model as a Markov chain on permutations. We will see that in many cases, and in particular for w an "evil-avoiding" permutation, the steady state probability of w can be expressed in terms of Schubert polynomials. Based on joint work with Donghyun Kim.

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Schubert Polynomials, The Inhomogeneous TASEP, And Evil-Avoiding Permutations

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