Schubert polynomials, the inhomogeneous TASEP, and evilavoiding 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
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Schubert Polynomials, The Inhomogeneous TASEP, And EvilAvoiding Permutations
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 "evilavoiding" permutation, the steady state probability of w can be expressed in terms of Schubert polynomials. Based on joint work with Donghyun Kim.
Schubert polynomials, the inhomogeneous TASEP, and evilavoiding permutations

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Schubert Polynomials, The Inhomogeneous TASEP, And EvilAvoiding Permutations
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