{
  "id": "1106.4468",
  "version": "v2",
  "published": "2011-06-22T14:44:26.000Z",
  "updated": "2012-04-12T10:33:23.000Z",
  "title": "Internal Aggregation Models on Comb Lattices",
  "authors": [
    "Wilfried Huss",
    "Ecaterina Sava"
  ],
  "comment": "23 pages, 4 figures",
  "journal": "Electronic Journal of Probability, 17 (2012), no. 30, page 1-21",
  "categories": [
    "math.PR"
  ],
  "abstract": "The two-dimensional comb lattice $C_2$ is a natural spanning tree of the Euclidean lattice $\\mathbb{Z}^2$. We study three related cluster growth models on $C_2$: internal diffusion limited aggregation (IDLA), in which random walkers move on the vertices of $C_2$ until reaching an unoccupied site where they stop; rotor-router aggregation in which particles perform deterministic walks, and stop when reaching a site previously unoccupied; and the divisible sandpile model where at each vertex there is a pile of sand, for which, at each step, the mass exceeding 1 is distributed equally among the neighbours. We describe the shape of the divisible sandpile cluster on $C_2$, which is then used to give inner bounds for IDLA and rotor-router aggregation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-12T10:33:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "05C81"
    ],
    "keywords": [
      "internal aggregation models",
      "particles perform deterministic walks",
      "rotor-router aggregation",
      "two-dimensional comb lattice",
      "random walkers move"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.4468H"
    }
  }
}