{
  "id": "1310.5099",
  "version": "v1",
  "published": "2013-10-18T17:23:24.000Z",
  "updated": "2013-10-18T17:23:24.000Z",
  "title": "Random Walks on Simplicial Complexes and Harmonics",
  "authors": [
    "Sayan Mukherjee",
    "John Steenbergen"
  ],
  "categories": [
    "math.CO",
    "math.PR",
    "math.SP"
  ],
  "abstract": "In this paper, we introduce random walks with absorbing states on simplicial complexes. Given a simplicial complex of dimension $d$, a random walk with an absorbing state is defined which relates to the spectrum of the $k$-dimensional Laplacian for $1 \\leq k \\leq d$ and which relates to the local random walk on a graph defined by Fan Chung. We also examine an application of random walks on simplicial complexes to a semi-supervised learning problem. Specifically, we consider a label propagation algorithm on oriented edges, which applies to a generalization of the partially labelled classification problem on graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-18T17:23:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C81",
      "55U10",
      "35P05",
      "55N10"
    ],
    "keywords": [
      "simplicial complexes",
      "absorbing state",
      "label propagation algorithm",
      "local random walk",
      "partially labelled classification problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.5099M"
    }
  }
}