{
  "id": "1210.7989",
  "version": "v1",
  "published": "2012-10-30T13:01:38.000Z",
  "updated": "2012-10-30T13:01:38.000Z",
  "title": "An explicit effect of non-symmetry of random walks on the triangular lattice",
  "authors": [
    "Satoshi Ishiwata",
    "Hiroshi Kawabi",
    "Tsubasa Teruya"
  ],
  "comment": "24pages, 4figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "In the present paper, we study an explicit effect of non-symmetry on asymptotics of the $n$-step transition probability as $n\\rightarrow \\infty$ for a class of non-symmetric random walks on the triangular lattice. Realizing the triangular lattice into $\\mathbb{R}^2$ appropriately, we observe that the Euclidean distance in $\\mathbb{R}^2$ naturally appears in the asymptotics. We characterize this realization from a geometric view point of Kotani-Sunada's standard realization of crystal lattices. As a corollary of the main theorem, we prove that the transition semigroup generated by the non-symmetric random walk approximates the heat semigroup generated by the usual Brownian motion on $\\mathbb{R}^2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-30T13:01:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "60F05",
      "60G50"
    ],
    "keywords": [
      "triangular lattice",
      "explicit effect",
      "non-symmetry",
      "non-symmetric random walk approximates",
      "geometric view point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.7989I"
    }
  }
}