{
  "id": "math/0503592",
  "version": "v1",
  "published": "2005-03-25T11:18:11.000Z",
  "updated": "2005-03-25T11:18:11.000Z",
  "title": "Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm",
  "authors": [
    "Richard F. Bass",
    "Xia Chen"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/009117904000000504 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2004, Vol. 32, No. 4, 3221-3247",
  "doi": "10.1214/009117904000000504",
  "categories": [
    "math.PR"
  ],
  "abstract": "If \\beta_t is renormalized self-intersection local time for planar Brownian motion, we characterize when Ee^{\\gamma\\beta_1} is finite or infinite in terms of the best constant of a Gagliardo-Nirenberg inequality. We prove large deviation estimates for \\beta_1 and -\\beta_1. We establish lim sup and lim inf laws of the iterated logarithm for \\beta_t as t\\to\\infty.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-25T11:18:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J55",
      "60J55",
      "60F10"
    ],
    "keywords": [
      "iterated logarithm",
      "critical exponent",
      "renormalized self-intersection local time",
      "planar brownian motion",
      "lim inf laws"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3592B"
    }
  }
}