{
  "id": "2410.18504",
  "version": "v1",
  "published": "2024-10-24T07:49:49.000Z",
  "updated": "2024-10-24T07:49:49.000Z",
  "title": "Glauber dynamics and coupling-from-the-past for Gaussian fields",
  "authors": [
    "Corentin Faipeur"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we study a centered Gaussian field on $\\mathbb{Z}^d$ defined by the following: the conditional law of the field at any site $i \\in \\mathbb{Z}^d$ is Gaussian of mean $\\epsilon$ times the mean of the neighbours, and of variance 1. We show that when $\\epsilon$ is small enough, this model can be written as a factor of an i.i.d. process, and that it is exponentially close to a finitely dependent model. Furthermore, if the field is conditioned to take values in a compact, we show that the factor can be realised with exponential tails.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-24T07:49:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "glauber dynamics",
      "coupling-from-the-past",
      "exponential tails",
      "centered gaussian field",
      "finitely dependent model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}