{
  "id": "1303.3381",
  "version": "v3",
  "published": "2013-03-14T09:11:27.000Z",
  "updated": "2016-02-22T12:46:21.000Z",
  "title": "Discrete versions of the transport equation and the Shepp-Olkin conjecture",
  "authors": [
    "Erwan Hillion",
    "Oliver Johnson"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/14-AOP973 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2016, Vol. 44, No. 1, 276-306",
  "doi": "10.1214/14-AOP973",
  "categories": [
    "math.PR",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "We introduce a framework to consider transport problems for integer-valued random variables. We introduce weighting coefficients which allow us to characterize transport problems in a gradient flow setting, and form the basis of our introduction of a discrete version of the Benamou-Brenier formula. Further, we use these coefficients to state a new form of weighted log-concavity. These results are applied to prove the monotone case of the Shepp-Olkin entropy concavity conjecture.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-02-11T18:33:38.000Z",
      "title": "Discrete versions of the transport equation and the Shepp--Olkin conjecture",
      "abstract": "We introduce a framework to consider transport problems for integer-valued random variables. We introduce weighting coefficients which allow us to characterise transport problems in a gradient flow setting, and form the basis of our introduction of a discrete version of the Benamou--Brenier formula. Further, we use these coefficients to state a new form of weighted log-concavity. These results are applied to prove the monotone case of the Shepp--Olkin entropy concavity conjecture.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-02-22T12:46:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discrete version",
      "shepp-olkin conjecture",
      "transport equation",
      "shepp-olkin entropy concavity conjecture",
      "characterise transport problems"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.3381H"
    }
  }
}