{
  "id": "1007.4779",
  "version": "v1",
  "published": "2010-07-27T18:07:41.000Z",
  "updated": "2010-07-27T18:07:41.000Z",
  "title": "A probabilistic interpretation of the Macdonald polynomials",
  "authors": [
    "Persi Diaconis",
    "Arun Ram"
  ],
  "categories": [
    "math.PR",
    "math.CO",
    "math.RT"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-27T18:07:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "probabilistic interpretation",
      "markov chain",
      "two-parameter macdonald polynomials",
      "auxiliary variables algorithm",
      "power sum polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.4779D"
    }
  }
}