University of Connecticut

Discrete Mathematics and Statistical Mechanics Seminar


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Title: Combinatorics of the 2-ASEP on a ring
Seminar Framework : Reading Group
Speaker: Olya Mandelshtam (Brown University)
Time: Thursday, March 22, 2018 at 2:30 pm
Place: MONT 214Abstract: The two-species asymmetric simple exclusion process (2-ASEP) on a ring is a Markov chain on Z/nZ 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 (Universite Paris-Diderot) and Lauren Williams (Berkeley).

Organizer: Zhongyang Li