{
  "id": "1307.6385",
  "version": "v4",
  "published": "2013-07-24T11:19:51.000Z",
  "updated": "2013-12-01T16:10:07.000Z",
  "title": "Hydrodynamic limit in a particle system with topological interactions",
  "authors": [
    "Gioia Carinci",
    "Anna De Masi",
    "Cristian Giardinà",
    "Errico Presutti"
  ],
  "comment": "45 pages, 2 figures",
  "categories": [
    "math.PR",
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study a system of particles in the interval $[0,\\epsilon^{-1}] \\cap \\mathbb Z$, $\\epsilon^{-1}$ a positive integer. The particles move as symmetric independent random walks (with reflections at the endpoints); simultaneously new particles are injected at site 0 at rate $j\\epsilon$ ($j>0$) and removed at same rate from the rightmost occupied site. The removal mechanism is therefore of topological rather than metric nature. The determination of the rightmost occupied site requires a knowledge of the entire configuration and prevents from using correlation functions techniques. We prove using stochastic inequalities that the system has a hydrodynamic limit, namely that under suitable assumptions on the initial configurations, the law of the density fields $\\epsilon \\sum \\phi(\\epsilon x) \\xi_{\\epsilon^{-2}t}(x)$ ($\\phi$ a test function, $\\xi_t(x)$ the number of particles at site $x$ at time $t$) concentrates in the limit $\\epsilon\\to 0$ on the deterministic value $\\int \\phi \\rho_t$, $\\rho_t$ interpreted as the limit density at time $t$. We characterize the limit $\\rho_t$ as a weak solution in terms of barriers of a limit free boundary problem.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-12-01T16:10:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hydrodynamic limit",
      "particle system",
      "topological interactions",
      "rightmost occupied site",
      "symmetric independent random walks"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.6385C"
    }
  }
}