Combinatorics Seminar: Combinatorics of the 2-ASEP on a ring

Seminar | February 26 | 12-1 p.m. | 939 Evans Hall

 Olya Mandelshtam, Brown University

 Department of Mathematics

The two-species asymmetric simple exclusion process (2-ASEP) on a ring is a Markov chain on Zn/Z with each site either vacant or occupied by one of two classes of particles, and whose dynamics are dictated by parameter q: particles can hop right at rate 1 or left at rate q. At q=0, the stationary probabilities of the states of the 2-ASEP can be described by multiline queues of Ferarri and Martin. We show a new combinatorial description of these probabilities in terms of certain cylindric tableaux which are in bijection with the multiline queues. We then extend this result for general q, which furthermore gives a combinatorial formula for certain non-symmetric Macdonald polynomials and proves a positivity conjecture in some special cases. This talk is based on ongoing work with Sylvie Corteel (University Paris-Diderot) and Lauren Williams (Berkeley).