{
  "id": "math/0608051",
  "version": "v1",
  "published": "2006-08-02T09:24:09.000Z",
  "updated": "2006-08-02T09:24:09.000Z",
  "title": "Equilibrium Glauber dynamics of continuous particle systems as a scaling limit of Kawasaki dynamics",
  "authors": [
    "Dmitri L. Finkelshtein",
    "Yuri G. Kondratiev",
    "Eugene W. Lytvynov"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "A Kawasaki dynamics in continuum is a dynamics of an infinite system of interacting particles in $\\mathbb{R}^d$ which randomly hop over the space. In this paper, we deal with an equilibrium Kawasaki dynamics which has a Gibbs measure $mu$ as invariant measure. We study a scaling limit of such a dynamics, derived through a scaling of the jump rate. Informally, we expect that, in the limit, only jumps of ``infinite length'' will survive, i.e., we expect to arrive at a Glauber dynamics in continuum (a birth-and-death process in $\\mathbb{R}^d$). We prove that, in the low activity-high temperature regime, the generators of the Kawasaki dynamics converge to the generator of a Glauber dynamics. The convergence is on the set of exponential functions, in the $L^2(\\mu)$-norm. Furthermore, additionally assuming that the potential of pair interaction is positive, we prove the weak convergence of the finite-dimensional distributions of the processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-08-02T09:24:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60J75",
      "60J80",
      "82C21",
      "82C22"
    ],
    "keywords": [
      "equilibrium glauber dynamics",
      "continuous particle systems",
      "scaling limit",
      "low activity-high temperature regime",
      "equilibrium kawasaki dynamics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8051F"
    }
  }
}