{
  "id": "1206.3856",
  "version": "v2",
  "published": "2012-06-18T09:01:21.000Z",
  "updated": "2016-03-15T10:23:00.000Z",
  "title": "Noise-stability and central limit theorems for effective resistance of random electric networks",
  "authors": [
    "Raphaël Rossignol"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/14-AOP996 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2016, Vol. 44, No. 2, 1053-1106",
  "doi": "10.1214/14-AOP996",
  "categories": [
    "math.PR"
  ],
  "abstract": "We investigate the (generalized) Walsh decomposition of point-to-point effective resistances on countable random electric networks with i.i.d. resistances. We show that it is concentrated on low levels, and thus point-to-point effective resistances are uniformly stable to noise. For graphs that satisfy some homogeneity property, we show in addition that it is concentrated on sets of small diameter. As a consequence, we compute the right order of the variance and prove a central limit theorem for the effective resistance through the discrete torus of side length $n$ in $\\mathbb {Z}^d$, when $n$ goes to infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-18T09:01:21.000Z",
      "abstract": "We investigate the (generalized) Walsh decomposition of point-to-point effective resistances on countable random electric networks with i.i.d resistances. We show that it is concentrated on low levels, and thus point-to-point effective resistances are uniformly stable to noise. For graphs that satisfy some homogeneity property, we show in addition that it is concentrated on sets of small diameter. As a consequence, we compute the right order of the variance and prove a central limit theorem for the effective resistance through the discrete torus of side $n$ in $\\mathcal{Z}^d$, when $n$ goes to infinity.",
      "comment": null,
      "journal": null,
      "doi": null,
      "authors": [
        "Raphael Rossignol"
      ]
    },
    {
      "version": "v2",
      "updated": "2016-03-15T10:23:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "central limit theorem",
      "point-to-point effective resistances",
      "noise-stability",
      "countable random electric networks",
      "low levels"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.3856R"
    }
  }
}