{
  "id": "1010.3579",
  "version": "v1",
  "published": "2010-10-18T12:32:41.000Z",
  "updated": "2010-10-18T12:32:41.000Z",
  "title": "Local limit theorems in free probability theory",
  "authors": [
    "Jiun-Chau Wang"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/09-AOP505 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2010, Vol. 38, No. 4, 1492-1506",
  "doi": "10.1214/09-AOP505",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we study the superconvergence phenomenon in the free central limit theorem for identically distributed, unbounded summands. We prove not only the uniform convergence of the densities to the semicircular density but also their $L^p$-convergence to the same limit for $p>1/2$. Moreover, an entropic central limit theorem is obtained as a consequence of the above results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-18T12:32:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free probability theory",
      "local limit theorems",
      "free central limit theorem",
      "entropic central limit theorem",
      "superconvergence phenomenon"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.3579W"
    }
  }
}