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MIT Combinatorics Seminar

Tableaux Combinatorics for the Asymmetric Exclusion Process


Lauren K. Williams (Harvard University)

Friday, March 24, 2006   4:30 PM;   Building 2 Room 105; 

ABSTRACT

The partially asymmetric exclusion process (PASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one-dimensional lattice of n sites. It is partially asymmetric in the sense that the probability of hopping left is q times the probability of hopping right. In this talk we will describe a surprising connection between the PASEP model and the combinatorics of certain 0-1 tableaux called permutation tableaux. Namely, we prove that in the long time limit, the probability that the PASEP model is in a particular configuration tau is essentially the weight generating function for permutation tableaux of shape lambda(tau).

This result suggests a connection between the PASEP model and total positivity for the Grassmannian (via work of Postnikov). Additionally, there should be connections to Stanley's theory of differential posets.