{
  "id": "2208.09835",
  "version": "v1",
  "published": "2022-08-21T08:01:53.000Z",
  "updated": "2022-08-21T08:01:53.000Z",
  "title": "A toy model for DLA arm growth in a wedge",
  "authors": [
    "Oren Louidor",
    "Chanwoo Oh",
    "Eviatar B. Procaccia"
  ],
  "comment": "8 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we consider a non-homogeneous discrete-time Markov chain which can be seen as a toy model for the growth of the arms of the DLA (Diffusion limited aggregation) process in a sub-linear wedge. It is conjectured that in a thin enough linear wedge there is only one infinite arm in the DLA cluster and we demonstrate this phenomenon in our model. The technique follows a bootstrapping argument, in which we iteratively prove ever faster growth rate.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-21T08:01:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dla arm growth",
      "toy model",
      "non-homogeneous discrete-time markov chain",
      "faster growth rate",
      "diffusion limited aggregation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}