Event Type
Seminar
Wednesday, April 21, 2021 2:00 PM
Donghyun Kim

The inhomogeneous totally asymmetric simple exclusion process (or TASEP) is a Markov chain on the set of permutations, in which adjacent numbers i and j swap places at rate x_i - y_j if the larger number is clockwise of the smaller. Conjecturally, steady state probabilities can be written as a positive sum of (double) Schubert polynomials. We will start by giving some background on this model, including Cantini's result showing that the inhomogeneous TASEP is a solvable lattice model. We will then use his result to show that a large number of states -- those corresponding to the "evil-avoiding" permutations (permutations avoiding patterns 2413, 4132, 4213, 3214) -- have steady state probabilities which are proportional to a product of Schubert polynomials.

Based on joint work with Lauren Williams.

Zoom link: https://stanford.zoom.us/j/91274693500?pwd=bmtHZnhTMG1HQ3pTOHYxUWJ2Z1ZjQT09
Zoom ID: 912 7469 3500
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