{
  "id": "1711.01248",
  "version": "v1",
  "published": "2017-11-03T17:23:43.000Z",
  "updated": "2017-11-03T17:23:43.000Z",
  "title": "Reaction-diffusion on the fully-connected lattice: $A+A\\rightarrow A$",
  "authors": [
    "L. Turban",
    "J. -Y. Fortin"
  ],
  "comment": "24 pages, 9 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong fluctuations in low dimensions. In this work we study this problem on the fully-connected lattice, an infinite-dimensional system in the thermodynamic limit, for which mean-field behaviour is expected. Exact expressions for the particle density distribution at a given time and survival time distribution for a given number of particles are obtained. In particular we show that the time needed to reach a finite number of surviving particles (vanishing density in the scaling limit) displays strong fluctuations and extreme value statistics, characterized by a universal class of non-Gaussian distributions with singular behaviour.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-03T17:23:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fully-connected lattice",
      "reaction-diffusion",
      "processes display non-equilibrium properties",
      "displays strong fluctuations",
      "particle density distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}