{
  "id": "0810.4113",
  "version": "v2",
  "published": "2008-10-22T17:08:06.000Z",
  "updated": "2008-11-03T13:30:33.000Z",
  "title": "Localization of maximal entropy random walk",
  "authors": [
    "Z. Burda",
    "J. Duda",
    "J. M. Luck",
    "B. Waclaw"
  ],
  "comment": "4 pages, 3 figures, minor changes in the discussion at the end of the paper",
  "journal": "Phys. Rev. Lett. 102, 160602 (2009)",
  "doi": "10.1103/PhysRevLett.102.160602",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "We define a new class of random walk processes which maximize entropy. This maximal entropy random walk is equivalent to generic random walk if it takes place on a regular lattice, but it is not if the underlying lattice is irregular. In particular, we consider a lattice with weak dilution. We show that the stationary probability of finding a particle performing maximal entropy random walk localizes in the largest nearly spherical region of the lattice which is free of defects. This localization phenomenon, which is purely classical in nature, is explained in terms of the Lifshitz states of a certain random operator.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-11-03T13:30:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.40.Fb",
      "72.15.Rn",
      "89.70.Cf"
    ],
    "keywords": [
      "localization",
      "maximal entropy random walk localizes",
      "performing maximal entropy random walk",
      "particle performing maximal entropy random",
      "generic random walk"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review Letters",
      "year": 2009,
      "month": "Apr",
      "volume": 102,
      "number": 16,
      "pages": 160602
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009PhRvL.102p0602B"
    }
  }
}