{
  "id": "1703.07541",
  "version": "v1",
  "published": "2017-03-22T06:34:48.000Z",
  "updated": "2017-03-22T06:34:48.000Z",
  "title": "Directed percolation and directed animals",
  "authors": [
    "Deepak Dhar"
  ],
  "comment": "Lecture notes of a school held at I.S.I. Delhi, 1996",
  "journal": "Published as a Chapter in \"Percolation theory and particle systems\", Ed. R. Roy, [Universities Press Hyderabad, 2000]",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "These lectures provide an introduction to the directed percolation and directed animals problems, from a physicist's point of view. The probabilistic cellular automaton formulation of directed percolation is introduced. The planar duality of the diode-resistor-insulator percolation problem in two dimensions, and relation of the directed percolation to undirected first passage percolation problem are described. Equivalence of the $d$-dimensional directed animals problem to $(d-1)$-dimensional Yang-Lee edge-singularity problem is established. Self-organized critical formulation of the percolation problem, which does not involve any fine-tuning of coupling constants to get critical behavior is briefly discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-22T06:34:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "directed percolation",
      "undirected first passage percolation problem",
      "probabilistic cellular automaton formulation",
      "dimensional yang-lee edge-singularity problem",
      "diode-resistor-insulator percolation problem"
    ],
    "tags": [
      "lecture notes",
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}