{
  "id": "1505.02049",
  "version": "v1",
  "published": "2015-05-08T14:34:28.000Z",
  "updated": "2015-05-08T14:34:28.000Z",
  "title": "Monotonicity and Condensation in Homogeneous Stochastic Particle Systems",
  "authors": [
    "Thomas Rafferty",
    "Paul Chleboun",
    "Stefan Grosskinsky"
  ],
  "comment": "25 pages, 3 figures",
  "categories": [
    "cond-mat.stat-mech",
    "math.PR"
  ],
  "abstract": "We study stochastic particle systems that conserve the particle density and exhibit a condensation transition due to particle interactions. We restrict our analysis to spatially homogeneous systems on finite lattices with stationary product measures, which includes previously studied zero-range or misanthrope processes. All known examples of such condensing processes are non-monotone, i.e. the dynamics do not preserve a partial ordering of the state space and the canonical measures (with a fixed number of particles) are not monotonically ordered. For our main result we prove that homogeneous particle systems with finite critical density are necessarily non-monotone. For infinite critical density condensation can still occur on finite lattices, in this case there also exist monotone condensing processes which we discuss in detail for power law tails.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-08T14:34:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "homogeneous stochastic particle systems",
      "study stochastic particle systems",
      "monotonicity",
      "finite lattices",
      "stationary product measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150502049R"
    }
  }
}