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• W2949824247 abstract "The two-parameter Macdonald polynomials are a central object of algebraic combinatorics and representation theory. We give a Markov chain on partitions of k with eigenfunctions the coefficients of the Macdonald polynomials when expanded in the power sum polynomials. The Markov chain has stationary distribution a new two-parameter family of measures on partitions, the inverse of the Macdonald weight (rescaled). The uniform distribution on permutations and the Ewens sampling formula are special cases. The Markov chain is a version of the auxiliary variables algorithm of statistical physics. Properties of the Macdonald polynomials allow a sharp analysis of the running time. In natural cases, a bounded number of steps suffice for arbitrarily large k." @default.
• W2949824247 created "2019-06-27" @default.
• W2949824247 creator A5001599475 @default.
• W2949824247 creator A5050449040 @default.
• W2949824247 date "2010-07-27" @default.
• W2949824247 modified "2023-09-27" @default.
• W2949824247 title "A probabilistic interpretation of the Macdonald polynomials" @default.
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