Evènement pour le groupe Combinatoire Énumérative et Algébrique

Date 2018-05-25  10:45-11:45
TitreCombinatorics of the ASEP on a ring 
RésuméThe m-species asymmetric simple exclusion process (m-ASEP) on a ring is a Markov chain on a ring with n sites with each site either vacant or occupied by one of m 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 m-ASEP can be described by multiline queues of Ferarri and Martin. For the 2-ASEP, 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 some classes of Macdonald polynomials. This talk is based on ongoing work with Sylvie Corteel (Université Paris-Diderot) and Lauren Williams (Berkeley).  
OrateurOlya Mandelshtam 
UrlUniversité Brown, Providence, États-Unis 

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