{
  "id": "math/0404089",
  "version": "v1",
  "published": "2004-04-05T15:09:54.000Z",
  "updated": "2004-04-05T15:09:54.000Z",
  "title": "Diffusion limited aggregation on a tree",
  "authors": [
    "MArtin T. Barlow",
    "Robin Pemantle",
    "Edwin A. Perkins"
  ],
  "comment": "56 pages",
  "journal": "Prob. Th. Rel. Fields, 107, 1 - 60 (1997)",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the following growth model on a regular d-ary tree. Points at distance n adjacent to the existing subtree are added with probabilities proportional to alpha^{-n}, where alpha<1 is a positive real parameter. The heights of these clusters are shown to increase linearly with their total size; this complements known results that show the height increases only logarithmically when alpha>=1. Results are obtained using stochastic monotonicity and regeneration results which may be of independent interest. Our motivation comes from two other ways in which the model may be viewed: as a problem in first-passage percolation, and as a version of diffusion-limited aggregation (DLA), adjusted so that `fingering' occurs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-04-05T15:09:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K40",
      "60K30",
      "60F05",
      "60F15",
      "60K35"
    ],
    "keywords": [
      "diffusion limited aggregation",
      "regular d-ary tree",
      "first-passage percolation",
      "motivation comes",
      "growth model"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 56,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......4089B"
    }
  }
}