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Tableaux combinatorics for the asymmetric exclusion process (ASEP)

Mathematical Physics & Probability

Speaker: Lauren Williams, UC Berkeley and Harvard University
Location: 1147 MSB
Start time: Wed, Jan 20 2010, 4:10PM

The ASEP is a model from statistical mechanics which describes a system of interacting particles hopping left and right on a one-dimensional lattice of n sites with open boundaries. In the bulk, the rate of hopping left is q times the rate of hopping right, and particles may enter and exit at both sides of the lattice at rates alpha, beta, gamma, and delta. We introduce some new tableaux (staircase tableaux) and use them to describe the stationary distribution of the ASEP with all parameters general. In special cases (gamma=delta=0) we can also "lift" the dynamics of the ASEP to a process on the tableaux themselves. Finally, using work of Uchiyama-Sasamoto-Wadati, we use our tableaux to give a combinatorial formula for moments of the Askey-Wilson weight function. This is joint work w/ Sylvie Corteel.