{
  "id": "1311.2726",
  "version": "v3",
  "published": "2013-11-12T09:51:15.000Z",
  "updated": "2014-01-29T10:03:56.000Z",
  "title": "Thermodynamic formalism and large deviations for multiplication-invariant potentials on lattice spin systems",
  "authors": [
    "J. -R. Chazottes",
    "F. Redig"
  ],
  "comment": "26 pages, 1 figure. To appear in the Electronic Journal of Probability",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We introduce the multiplicative Ising model and prove basic properties of its thermodynamic formalism such as existence of pressure and entropies. We generalize to one-dimensional \"layer-unique\" Gibbs measures for which the same results can be obtained. For more general models associated to a $d$-dimensional multiplicative invariant potential, we prove a large deviation theorem in the uniqueness regime for averages of multiplicative shifts of general local functions. This thermodynamic formalism is motivated by the statistical properties of multiple ergodic averages.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-01-29T10:03:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "thermodynamic formalism",
      "lattice spin systems",
      "multiplication-invariant potentials",
      "multiple ergodic averages",
      "general local functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.2726C"
    }
  }
}