{
  "id": "1512.09035",
  "version": "v1",
  "published": "2015-12-30T17:47:20.000Z",
  "updated": "2015-12-30T17:47:20.000Z",
  "title": "Long time behaviour of random walks on the integer lattice",
  "authors": [
    "Bartosz Trojan"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider an irreducible finite range random walk on the $d$-dimensional integer lattice and study asymptotic behaviour of its transition function $p(n; x)$. In particular, for simple random walk our asymptotic formula is valid as long as $n (n - |x|_1)^{-2}$ tends to zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-30T17:47:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "60F05",
      "60F99",
      "60B10"
    ],
    "keywords": [
      "long time behaviour",
      "irreducible finite range random walk",
      "study asymptotic behaviour",
      "simple random walk",
      "dimensional integer lattice"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151209035T"
    }
  }
}