{
  "id": "1001.2533",
  "version": "v3",
  "published": "2010-01-14T19:10:02.000Z",
  "updated": "2010-12-04T17:46:36.000Z",
  "title": "Spiders in random environment",
  "authors": [
    "Christophe Gallesco",
    "Sebastian Muller",
    "Serguei Popov",
    "Marina Vachkovskaia"
  ],
  "comment": "25 pages, 5 figures",
  "doi": "10.1051/ps/2010008",
  "categories": [
    "math.PR"
  ],
  "abstract": "A spider consists of several, say $N$, particles. Particles can jump independently according to a random walk if the movement does not violate some given restriction rules. If the movement violates a rule it is not carried out. We consider random walk in random environment (RWRE) on $\\Z$ as underlying random walk. We suppose the environment $\\omega=(\\omega_x)_{x \\in \\Z}$ to be elliptic, with positive drift and nestling, so that there exists a unique positive constant $\\kappa$ such that $\\E[((1-\\omega_0)/\\omega_0)^{\\kappa}]=1$. The restriction rules are kept very general; we only assume transitivity and irreducibility of the spider. The main result is that the speed of a spider is positive if $\\kappa/N>1$ and null if $\\kappa/N<1$. In particular, if $\\kappa/N <1$ a spider has null speed but the speed of a (single) RWRE is positive.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-12-04T17:46:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37"
    ],
    "keywords": [
      "random environment",
      "restriction rules",
      "movement violates",
      "underlying random walk",
      "spider consists"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.2533G"
    }
  }
}