{
  "id": "1207.1574",
  "version": "v1",
  "published": "2012-07-06T10:11:56.000Z",
  "updated": "2012-07-06T10:11:56.000Z",
  "title": "A particle system with explosions: law of large numbers for the density of particles and the blow-up time",
  "authors": [
    "Tertuliano Franco",
    "Pablo Groisman"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider a system of independent random walks in the discrete torus with creation-annihilation of particles and possible explosion of the total number of particles in finite time. Rescaling space and rates for diffusion/creation/annihilation of particles, we obtain a stong law of large numbers for the density of particles in the supremum norm. The limiting object is a classical solution to the semilinear heat equation u_t =u_{xx} + f(u). If f(u)=u^p, 1<p \\le 3, we also obtain a law of large numbers for the explosion time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-06T10:11:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "35K55",
      "35B40"
    ],
    "keywords": [
      "large numbers",
      "particle system",
      "blow-up time",
      "independent random walks",
      "semilinear heat equation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s10955-012-0621-8",
      "journal": "Journal of Statistical Physics",
      "year": 2012,
      "month": "Nov",
      "volume": 149,
      "number": 4,
      "pages": 629
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JSP...149..629F"
    }
  }
}