{
  "id": "1211.7125",
  "version": "v3",
  "published": "2012-11-30T00:15:43.000Z",
  "updated": "2014-04-28T13:50:00.000Z",
  "title": "Moments and Lyapunov exponents for the parabolic Anderson model",
  "authors": [
    "Alexei Borodin",
    "Ivan Corwin"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/13-AAP944 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2014, Vol. 24, No. 3, 1172-1198",
  "doi": "10.1214/13-AAP944",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the parabolic Anderson model in $(1+1)$ dimensions with nearest neighbor jumps and space-time white noise (discrete space/continuous time). We prove a contour integral formula for the second moment and compute the second moment Lyapunov exponent. For the model with only jumps to the right, we prove a contour integral formula for all moments and compute moment Lyapunov exponents of all orders.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-04-28T13:50:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "parabolic anderson model",
      "contour integral formula",
      "second moment lyapunov exponent",
      "space-time white noise",
      "nearest neighbor jumps"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.7125B"
    }
  }
}