{
  "id": "1011.2713",
  "version": "v2",
  "published": "2010-11-11T17:13:39.000Z",
  "updated": "2011-09-13T09:28:50.000Z",
  "title": "Fractional $P(φ)_1$-processes and Gibbs measures",
  "authors": [
    "Kamil Kaleta",
    "Jozsef Lorinczi"
  ],
  "comment": "37 pages",
  "journal": "Stochastic Process. Appl. 122 (10) (2012) 3580-3617",
  "doi": "10.1016/j.spa.2012.06.001",
  "categories": [
    "math.PR",
    "math.SP"
  ],
  "abstract": "We define and prove existence of fractional $P(\\phi)_1$-processes as random processes generated by fractional Schr\\\"odinger semigroups with Kato-decomposable potentials. Also, we show that the measure of such a process is a Gibbs measure with respect to the same potential. We give conditions of its uniqueness and characterize its support relating this with intrinsic ultracontractivity properties of the semigroup and the fall-off of the ground state. To achieve that we establish and analyze these properties first.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-09-13T09:28:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47D08",
      "47G30",
      "60G52"
    ],
    "keywords": [
      "gibbs measure",
      "fractional",
      "intrinsic ultracontractivity properties",
      "properties first",
      "ground state"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 877119,
      "adsabs": "2010arXiv1011.2713K"
    }
  }
}