# A probabilistic interpretation of the Macdonald polynomials

@article{Diaconis2010API, title={A probabilistic interpretation of the Macdonald polynomials}, author={Persi Diaconis and Arun Ram}, journal={Annals of Probability}, year={2010}, volume={40}, pages={1861-1896} }

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 cycles of permutations and the Ewens sampling formula are…

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