{
  "id": "1605.07575",
  "version": "v1",
  "published": "2016-05-24T18:32:49.000Z",
  "updated": "2016-05-24T18:32:49.000Z",
  "title": "How can a clairvoyant particle escape the exclusion process?",
  "authors": [
    "Rangel Baldasso",
    "Augusto Teixeira"
  ],
  "comment": "29 pages, 10 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study a detection problem in the following setting: on the integer lattice, at time zero, place nodes on each site independently with probability $\\rho \\in [0,1)$ and let them evolve as an exclusion process. At time zero, place a target at the origin. The target moves only at integer times, and can move to any site that is within distance R from its current position. Assume also that the target can predict the future movement of all nodes. We prove that, for R large enough (depending on the value of $\\rho$) it is possible for the target to avoid detection forever with positive probability. The proof of this result uses two ingredients of independent interest. First we establish a renormalisation scheme that can be used to prove percolation for dependent oriented models under a certain decoupling condition. The second step of the proof is a space-time decoupling for the exclusion process.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-24T18:32:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "60K35",
      "82B43",
      "82C22"
    ],
    "keywords": [
      "exclusion process",
      "clairvoyant particle escape",
      "time zero",
      "avoid detection forever",
      "place nodes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}