{
  "id": "1304.2449",
  "version": "v1",
  "published": "2013-04-09T02:32:15.000Z",
  "updated": "2013-04-09T02:32:15.000Z",
  "title": "On nonlinear Schrödinger equations with random potentials: existence and probabilistic properties",
  "authors": [
    "Leandro Cioletti",
    "Lucas C. F. Ferreira",
    "Marcelo Furtado"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "In this paper we are concerned with nonlinear Schr\\\"odinger equations with random potentials. Our class includes continuum and discrete potentials. Conditions on the potential $V_{\\omega}$ are found for existence of solutions almost sure $\\omega $. We study probabilistic properties like central limit theorem and law of larger numbers for the obtained solutions by independent ensembles. We also give estimates on the expected value for the $L^{\\infty}$-norm of the solution showing how it depends on the size of the potential.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-09T02:32:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B80",
      "60H25",
      "35J60",
      "35R60",
      "82B44",
      "47H10"
    ],
    "keywords": [
      "nonlinear schrödinger equations",
      "random potentials",
      "central limit theorem",
      "study probabilistic properties",
      "discrete potentials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.2449C"
    }
  }
}