{
  "id": "0812.4108",
  "version": "v3",
  "published": "2008-12-22T07:19:11.000Z",
  "updated": "2009-06-19T01:04:31.000Z",
  "title": "Non-Equilibrium Dynamics of Dyson's Model with an Infinite Number of Particles",
  "authors": [
    "Makoto Katori",
    "Hideki Tanemura"
  ],
  "comment": "v3: AMS-LaTeX, 32 pages, 1 figure, revised version for publication in Commun. Math. Phys",
  "journal": "Commun. Math. Phys. 293 (2010) 469-497",
  "doi": "10.1007/s00220-009-0912-3",
  "categories": [
    "math.PR",
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "Dyson's model is a one-dimensional system of Brownian motions with long-range repulsive forces acting between any pair of particles with strength proportional to the inverse of distances with proportionality constant $\\beta/2$. We give sufficient conditions for initial configurations so that Dyson's model with $\\beta=2$ and an infinite number of particles is well defined in the sense that any multitime correlation function is given by a determinant with a continuous kernel. The class of infinite-dimensional configurations satisfying our conditions is large enough to study non-equilibrium dynamics. For example, we obtain the relaxation process starting from a configuration, in which every point of $\\Z$ is occupied by one particle, to the stationary state, which is the determinantal point process with the sine kernel.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-06-19T01:04:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dysons model",
      "infinite number",
      "determinantal point process",
      "study non-equilibrium dynamics",
      "multitime correlation function"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Communications in Mathematical Physics",
      "year": 2010,
      "month": "Jan",
      "volume": 293,
      "number": 2,
      "pages": 469
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010CMaPh.293..469K"
    }
  }
}