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• W2034159031 abstract "We introduce some combinatorial objects called staircase tableaux, which have cardinality 4 n n !, and connect them to both the asymmetric exclusion process (ASEP) and Askey-Wilson polynomials. The ASEP is a model from statistical mechanics introduced in the late 1960s, which describes a system of interacting particles hopping left and right on a one-dimensional lattice of n sites with open boundaries. It has been cited as a model for traffic flow and translation in protein synthesis. In its most general form, particles may enter and exit at the left with probabilities α and γ, and they may exit and enter at the right with probabilities β and δ. In the bulk, the probability of hopping left is q times the probability of hopping right. Our first result is a formula for the stationary distribution of the ASEP with all parameters general, in terms of staircase tableaux. Our second result is a formula for the moments of (the weight function of) Askey-Wilson polynomials, also in terms of staircase tableaux. Since the 1980s there has been a great deal of work giving combinatorial formulas for moments of classical orthogonal polynomials (e.g. Hermite, Charlier, Laguerre); among these polynomials, the Askey-Wilson polynomials are the most important, because they are at the top of the hierarchy of classical orthogonal polynomials." @default.
• W2034159031 created "2016-06-24" @default.
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• W2034159031 date "2010-03-26" @default.
• W2034159031 modified "2023-10-02" @default.
• W2034159031 title "Staircase tableaux, the asymmetric exclusion process, and Askey-Wilson polynomials" @default.
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• W2034159031 doi "https://doi.org/10.1073/pnas.0909915107" @default.
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