{
  "id": "1712.06529",
  "version": "v1",
  "published": "2017-12-18T17:14:44.000Z",
  "updated": "2017-12-18T17:14:44.000Z",
  "title": "Non-criticality criteria for Abelian sandpile models with sources and sinks",
  "authors": [
    "Frank Redig",
    "Wioletta M. Ruszel",
    "Ellen Saada"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove that the Abelian sandpile model on a random binary and binomial tree, as introduced in \\cite{rrs}, is not critical for all branching probabilities $p<1$; by estimating the tail of the annealed survival time of a random walk on the binary tree with randomly placed traps, we obtain some more information about the exponential tail of the avalanche radius. Next we study the sandpile model on $\\Zd$ with some additional dissipative sites: we provide examples and sufficient conditions for non-criticality; we also make a connection with the parabolic Anderson model. Finally we initiate the study of the sandpile model with both sources and sinks and give a sufficient condition for non-criticality in the presence of a finite number of sources, using a connection with the homogeneous pinning model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-18T17:14:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian sandpile model",
      "non-criticality criteria",
      "sufficient condition",
      "parabolic anderson model",
      "binomial tree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}