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.
Description
[1007.4779] A probabilistic interpretation of the Macdonald polynomials
%0 Generic
%1 diaconis2010macdonald
%A Diaconis, Persi
%A Ram, Arun
%D 2010
%K ewens_sampling_formula mixing_times partitions representation_theory residual_allocation stick_breaking
%T A probabilistic interpretation of the Macdonald polynomials
%U http://arxiv.org/abs/1007.4779
%X 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.
@misc{diaconis2010macdonald,
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.
},
added-at = {2010-07-29T20:25:08.000+0200},
author = {Diaconis, Persi and Ram, Arun},
biburl = {https://www.bibsonomy.org/bibtex/2c12fef8edb47978327c9848962314619/peter.ralph},
description = {[1007.4779] A probabilistic interpretation of the Macdonald polynomials},
interhash = {72f15e04a222a0c4ad105aa58fbe155b},
intrahash = {c12fef8edb47978327c9848962314619},
keywords = {ewens_sampling_formula mixing_times partitions representation_theory residual_allocation stick_breaking},
note = {cite arxiv:1007.4779
},
timestamp = {2010-07-29T20:41:56.000+0200},
title = {A probabilistic interpretation of the {Macdonald} polynomials},
url = {http://arxiv.org/abs/1007.4779},
year = 2010
}