{
  "id": "1101.4765",
  "version": "v2",
  "published": "2011-01-25T10:38:36.000Z",
  "updated": "2011-06-15T10:42:29.000Z",
  "title": "Binary jumps in continuum. I. Equilibrium processes and their scaling limits",
  "authors": [
    "Dmitri L. Finkelshtein",
    "Yuri G. Kondratiev",
    "Oleksandr V. Kutoviy",
    "Eugene Lytvynov"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $\\Gamma$ denote the space of all locally finite subsets (configurations) in $R^d$. A stochastic dynamics of binary jumps in continuum is a Markov process on $\\Gamma$ in which pairs of particles simultaneously hop over $R^d$. In this paper, we study an equilibrium dynamics of binary jumps for which a Poisson measure is a symmetrizing (and hence invariant) measure. The existence and uniqueness of the corresponding stochastic dynamics are shown. We next prove the main result of this paper: a big class of dynamics of binary jumps converge, in a diffusive scaling limit, to a dynamics of interacting Brownian particles. We also study another scaling limit, which leads us to a spatial birth-and-death process in continuum. A remarkable property of the limiting dynamics is that its generator possesses a spectral gap, a property which is hopeless to expect from the initial dynamics of binary jumps.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-06-15T10:42:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "02.50.Ga",
      "05.40.Jc"
    ],
    "keywords": [
      "scaling limit",
      "equilibrium processes",
      "stochastic dynamics",
      "binary jumps converge",
      "spatial birth-and-death process"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1063/1.3601118",
      "journal": "Journal of Mathematical Physics",
      "year": 2011,
      "month": "Jun",
      "volume": 52,
      "number": 6,
      "pages": 3304
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011JMP....52f3304F"
    }
  }
}