{
  "id": "math/0112315",
  "version": "v3",
  "published": "2001-12-31T18:17:29.000Z",
  "updated": "2002-01-03T14:35:03.000Z",
  "title": "Hitting properties of a random string",
  "authors": [
    "Carl Mueller",
    "Roger Tribe"
  ],
  "journal": "Electronic J. Probab., 7, paper 10, 1-29, (2002)",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We consider Funaki's model of a random string taking values in R^d. It is specified by the following stochastic PDE, du = u_{xx} + W, where W=W(x,t) is two-parameter white noise, also taking values in R^d. We study hitting properties, double points, and recurrence. The main difficulty is that the process has the Markov property in time, but not in space. We find: (1) The string hits points if d<6. (2) For fixed t, there are points x,y such that u(t,x)=u(t,y) iff d < 4. (3) There exist points t,x,y such that u(t,x)=u(t,y) iff d < 8. (4) There exist points s,t,x,y such that u(t,x)=u(s,y) iff d < 12. (5) The string is recurrent iff d < 7.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2002-01-03T14:35:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "35R60",
      "35L05"
    ],
    "keywords": [
      "random string",
      "two-parameter white noise",
      "funakis model",
      "study hitting properties",
      "stochastic pde"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....12315M"
    }
  }
}