{
  "id": "1003.1001",
  "version": "v2",
  "published": "2010-03-04T10:17:29.000Z",
  "updated": "2010-03-26T03:03:25.000Z",
  "title": "Persistent Homology for Random Fields and Complexes",
  "authors": [
    "Robert J. Adler",
    "Omer Bobrowski",
    "Matthew S. Borman",
    "Eliran Subag",
    "Shmuel Weinberger"
  ],
  "categories": [
    "math.PR",
    "math.AT"
  ],
  "abstract": "We discuss and review recent developments in the area of applied algebraic topology, such as persistent homology and barcodes. In particular, we discuss how these are related to understanding more about manifold learning from random point cloud data, the algebraic structure of simplicial complexes determined by random vertices, and, in most detail, the algebraic topology of the excursion sets of random fields.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-03-26T03:03:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "55N35",
      "60G55",
      "62H35"
    ],
    "keywords": [
      "random fields",
      "persistent homology",
      "random point cloud data",
      "applied algebraic topology",
      "excursion sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.1001A"
    }
  }
}