{
  "id": "1603.01885",
  "version": "v1",
  "published": "2016-03-06T22:22:22.000Z",
  "updated": "2016-03-06T22:22:22.000Z",
  "title": "Increasing coupling of probabilistic cellular automata",
  "authors": [
    "Pierre-Yves Louis"
  ],
  "journal": "Statistics & Probability Letters, Volume 74, Issue 1, 1 August 2005, Pages 1--13",
  "doi": "10.1016/j.spl.2005.04.021",
  "categories": [
    "math.PR",
    "cond-mat.stat-mech"
  ],
  "abstract": "We give a necessary and sufficient condition for the existence of an increasing coupling of $N$ ($N \\geq 2$) synchronous dynamics on $S^{\\mathbb Z^d}$(PCA). Increasing means the coupling preserves stochastic ordering. We first present our main construction theorem in the case where $S$ is totally ordered, applications to attractive PCA's are given. When $S$ is only partially ordered, we show on two examples that a coupling of more than two synchronous dynamics may not exist. We also prove an extension of our main result for a particular class of partially ordered spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-06T22:22:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60E15",
      "60J10",
      "82C20",
      "37B15",
      "68W10"
    ],
    "keywords": [
      "probabilistic cellular automata",
      "increasing coupling",
      "synchronous dynamics",
      "main construction theorem",
      "main result"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160301885L"
    }
  }
}