{
  "id": "0805.0706",
  "version": "v2",
  "published": "2008-05-06T13:12:36.000Z",
  "updated": "2009-02-02T05:50:54.000Z",
  "title": "Principal eigenvalue for random walk among random traps on Z^d",
  "authors": [
    "Jean-Christophe Mourrat"
  ],
  "comment": "17 pages, v2: simplified proofs in section 3",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $(\\tau_x)_{x \\in \\Z^d}$ be i.i.d. random variables with heavy (polynomial) tails. Given $a \\in [0,1]$, we consider the Markov process defined by the jump rates $\\omega_{x \\to y} = {\\tau_x}^{-(1-a)} {\\tau_y}^a$ between two neighbours $x$ and $y$ in $\\Z^d$. We give the asymptotic behaviour of the principal eigenvalue of the generator of this process, with Dirichlet boundary condition. The prominent feature is a phase transition that occurs at some threshold depending on the dimension.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-02-02T05:50:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "82B41",
      "47A75"
    ],
    "keywords": [
      "principal eigenvalue",
      "random walk",
      "random traps",
      "dirichlet boundary condition",
      "phase transition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.0706M"
    }
  }
}