{
  "id": "1212.4447",
  "version": "v2",
  "published": "2012-12-18T17:54:13.000Z",
  "updated": "2013-05-14T01:31:18.000Z",
  "title": "Crossing speeds of random walks among \"sparse\" or \"spiky\" Bernoulli potentials on integers",
  "authors": [
    "Elena Kosygina"
  ],
  "comment": "24 pages, 1 figure",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a random walk among i.i.d. obstacles on the one dimensional integer lattice under the condition that the walk starts from the origin and reaches a remote location y. The obstacles are represented by a killing potential, which takes value M>0 with probability p and value 0 with probability (1-p), 0<p<1, independently at each site of the lattice. We consider the walk under both quenched and annealed measures. It is known that under either measure the crossing time from 0 to y of such walk, tau(y), grows linearly in y. More precisely, the expectation of tau(y)/y converges to a limit as y approaches infinity. The reciprocal of this limit is called the asymptotic speed of the conditioned walk. We study the behavior of the asymptotic speed in two regimes: (1) as p goes to 0 for M fixed (\"sparse\"), and (2) as M goes to infinity for p fixed (\"spiky\"). We observe and quantify a dramatic difference between the quenched and annealed settings.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-14T01:31:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "60F05",
      "60J80",
      "60J60"
    ],
    "keywords": [
      "random walk",
      "bernoulli potentials",
      "crossing speeds",
      "dimensional integer lattice",
      "walk starts"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s10955-013-0765-1",
      "journal": "Journal of Statistical Physics",
      "year": 2013,
      "month": "Jul",
      "volume": 152,
      "number": 2,
      "pages": 213
    },
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013JSP...152..213K"
    }
  }
}