{
  "id": "1202.1847",
  "version": "v1",
  "published": "2012-02-08T22:14:49.000Z",
  "updated": "2012-02-08T22:14:49.000Z",
  "title": "On the most visited sites of planar Brownian motion",
  "authors": [
    "Valentina Cammarota",
    "Peter Mörters"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Let (B_t : t > 0) be a planar Brownian motion and define gauge functions $\\phi_\\alpha(s)=log(1/s)^{-\\alpha}$ for $\\alpha>0$. If $\\alpha<1$ we show that almost surely there exists a point x in the plane such that $H^{\\phi_\\alpha}({t > 0 : B_t=x})>0$, but if $\\alpha>1$ almost surely $H^{\\phi_\\alpha} ({t > 0 : B_t=x})=0$ simultaneously for all $x\\in R^2$. This resolves a longstanding open problem posed by S.,J. Taylor in 1986.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-02-08T22:14:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65"
    ],
    "keywords": [
      "planar brownian motion",
      "visited sites",
      "define gauge functions",
      "longstanding open problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.1847C"
    }
  }
}