{
  "id": "1308.6193",
  "version": "v1",
  "published": "2013-08-28T16:03:50.000Z",
  "updated": "2013-08-28T16:03:50.000Z",
  "title": "Random walks on dynamical percolation: mixing times, mean squared displacement and hitting times",
  "authors": [
    "Yuval Peres",
    "Alexandre Stauffer",
    "Jeffrey E. Steif"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the behavior of random walk on dynamical percolation. In this model, the edges of a graph G are either open or closed and refresh their status at rate \\mu\\ while at the same time a random walker moves on G at rate 1 but only along edges which are open. On the d-dimensional torus with side length n, we prove that in the subcritical regime, the mixing times for both the full system and the random walker are n^2/\\mu\\ up to constants. We also obtain results concerning mean squared displacement and hitting times. Finally, we show that the usual recurrence transience dichotomy for the lattice Z^d holds for this model as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-28T16:03:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60K37"
    ],
    "keywords": [
      "dynamical percolation",
      "mixing times",
      "hitting times",
      "concerning mean squared displacement",
      "usual recurrence transience dichotomy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.6193P"
    }
  }
}