|Date||Apr 18, 2023|
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 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 back- ground on this model, including Cantini’s result showing that the inhomoge- neous 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” permu- tations (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.