{
  "id": "math/0501533",
  "version": "v2",
  "published": "2005-01-29T02:38:39.000Z",
  "updated": "2006-06-28T13:51:53.000Z",
  "title": "Shortest spanning trees and a counterexample for random walks in random environments",
  "authors": [
    "Maury Bramson",
    "Ofer Zeitouni",
    "Martin P. W. Zerner"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/009117905000000783 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. 3, 821-856",
  "doi": "10.1214/009117905000000783",
  "categories": [
    "math.PR"
  ],
  "abstract": "We construct forests that span $\\mathbb{Z}^d$, $d\\geq2$, that are stationary and directed, and whose trees are infinite, but for which the subtrees attached to each vertex are as short as possible. For $d\\geq3$, two independent copies of such forests, pointing in opposite directions, can be pruned so as to become disjoint. From this, we construct in $d\\geq3$ a stationary, polynomially mixing and uniformly elliptic environment of nearest-neighbor transition probabilities on $\\mathbb{Z}^d$, for which the corresponding random walk disobeys a certain zero--one law for directional transience.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-06-28T13:51:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "05C80",
      "82D30"
    ],
    "keywords": [
      "shortest spanning trees",
      "random environments",
      "counterexample",
      "nearest-neighbor transition probabilities",
      "corresponding random walk disobeys"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......1533B"
    }
  }
}