{
  "id": "1407.2317",
  "version": "v2",
  "published": "2014-07-09T00:07:30.000Z",
  "updated": "2015-06-04T23:37:22.000Z",
  "title": "Low Threshold Bootstrap Percolation on the Hamming Torus",
  "authors": [
    "Erik Slivken"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper analyzes various questions pertaining to bootstrap percolation on the $d$-dimensional Hamming torus where each node is open with probability $p$ and the percolation threshold is 2. For each $d'<d$ we find the critical exponent for the event that a $d'$-dimensional subtorus becomes open and compute the limiting value of its probability under the critical scaling. For even $d'$, we use the Chen-Stein method to show that the number of $d'$-dimensional subtori that become open can be approximated by a Poisson random variable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-09T00:07:30.000Z",
      "title": "Bootstrap Percolation on the Hamming Torus with Threshold 2",
      "abstract": "This paper analyzes various questions pertaining to bootstrap percolation on the d-dimension Hamming torus where each node is open with probability p. We find the critical exponent for the event that a 2j-dimension sublattice becomes open and compute exact limiting values for probabilities for the existence of such a 2j-dimension sublattice. We use Stein-Chen's method to show that the number of 2j-dimension sublattices that become open can be approximated by a Poisson random variable.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-06-04T23:37:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35"
    ],
    "keywords": [
      "bootstrap percolation",
      "2j-dimension sublattice",
      "probability",
      "d-dimension hamming torus",
      "paper analyzes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.2317S"
    }
  }
}