{
  "id": "math/0408060",
  "version": "v3",
  "published": "2004-08-04T15:53:27.000Z",
  "updated": "2007-05-24T10:59:11.000Z",
  "title": "Infinite volume limit of the Abelian sandpile model in dimensions d >= 3",
  "authors": [
    "Antal A. Jarai",
    "Frank Redig"
  ],
  "comment": "First version: LaTeX; 29 pages. Revised version: LaTeX; 29 pages. The main result of the paper has been extended to all dimensions at least 3, with a new and simplyfied proof of finiteness of the two-component spanning tree. Second revision: LaTeX; 32 pages",
  "journal": "Probab. Theory Related Fields 141 (2008), no. 1-2, 181-212",
  "doi": "10.1007/s00440-007-0083-0",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the Abelian sandpile model on Z^d. In dimensions at least 3 we prove existence of the infinite volume addition operator, almost surely with respect to the infinite volume limit mu of the uniform measures on recurrent configurations. We prove the existence of a Markov process with stationary measure mu, and study ergodic properties of this process. The main techniques we use are a connection between the statistics of waves and uniform two-component spanning trees and results on the uniform spanning tree measure on Z^d.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-05-24T10:59:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82C22"
    ],
    "keywords": [
      "abelian sandpile model",
      "dimensions",
      "infinite volume addition operator",
      "infinite volume limit mu",
      "uniform spanning tree measure"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......8060J"
    }
  }
}