{
  "id": "math/0503042",
  "version": "v2",
  "published": "2005-03-02T15:16:44.000Z",
  "updated": "2007-02-08T08:57:42.000Z",
  "title": "Equilibrium Kawasaki dynamics of continuous particle systems",
  "authors": [
    "Yu. G. Kondratiev",
    "E. Lytvynov",
    "M. Röckner"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We construct a new equilibrium dynamics of infinite particle systems in a Riemannian manifold $X$. This dynamics is an analog of the Kawasaki dynamics of lattice spin systems. The Kawasaki dynamics now is a process where interacting particles randomly hop over $X$. We establish conditions on the {\\it a priori} explicitly given symmetrizing measure and the generator of this dynamics, under which a corresponding conservative Markov processes exists. We also outline two types of scaling limit of the equilibrium Kawasaki dynamics: one leading to an equilibrium Glauber dynamics in continuum (a birth-and-death process), and the other leading to a diffusion dynamics of interacting particles (in particular, the gradient stochastic dynamics).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-02-08T08:57:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60J75",
      "60J80",
      "82C21",
      "82C22"
    ],
    "keywords": [
      "equilibrium kawasaki dynamics",
      "continuous particle systems",
      "gradient stochastic dynamics",
      "infinite particle systems",
      "equilibrium glauber dynamics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3042K"
    }
  }
}