{
  "id": "math/0403351",
  "version": "v2",
  "published": "2004-03-22T10:42:21.000Z",
  "updated": "2006-09-21T12:22:44.000Z",
  "title": "Hitting times for independent random walks on $\\mathbb{Z}^d$",
  "authors": [
    "Amine Asselah",
    "Pablo A. Ferrari"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/009117906000000106 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2006, Vol. 34, No. 4, 1296-1338",
  "doi": "10.1214/009117906000000106",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a system of asymmetric independent random walks on $\\mathbb{Z}^d$, denoted by $\\{\\eta_t,t\\in{\\mathbb{R}}\\}$, stationary under the product Poisson measure $\\nu_{\\rho}$ of marginal density $\\rho>0$. We fix a pattern $\\mathcal{A}$, an increasing local event, and denote by $\\tau$ the hitting time of $\\mathcal{A}$. By using a loss network representation of our system, at small density, we obtain a coupling between the laws of $\\eta_t$ conditioned on $\\{\\tau>t\\}$ for all times $t$. When $d\\ge3$, this provides bounds on the rate of convergence of the law of $\\eta_t$ conditioned on $\\{\\tau>t\\}$ toward its limiting probability measure as $t$ tends to infinity. We also treat the case where the initial measure is close to $\\nu_{\\rho}$ without being product.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-09-21T12:22:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82C22",
      "60J25"
    ],
    "keywords": [
      "hitting time",
      "asymmetric independent random walks",
      "product poisson measure",
      "loss network representation",
      "initial measure"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3351A"
    }
  }
}