{
  "id": "math/0609303",
  "version": "v1",
  "published": "2006-09-11T17:53:04.000Z",
  "updated": "2006-09-11T17:53:04.000Z",
  "title": "The simple random walk and max-degree walk on a directed graph",
  "authors": [
    "Ravi Montenegro"
  ],
  "journal": "Random Structures and Algorithms, vol 34:3, pp. 395-407, 2009.",
  "doi": "10.1002/rsa.20227",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "We show bounds on total variation and $L^{\\infty}$ mixing times, spectral gap and magnitudes of the complex valued eigenvalues of a general (non-reversible non-lazy) Markov chain with a minor expansion property. This leads to the first known bounds for the non-lazy simple and max-degree walks on a (directed) graph, and even in the lazy case they are the first bounds of the optimal order. In particular, it is found that within a factor of two or four, the worst case of each of these mixing time and eigenvalue quantities is a walk on a cycle with clockwise drift.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-09-11T17:53:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "68W20"
    ],
    "keywords": [
      "simple random walk",
      "max-degree walk",
      "directed graph",
      "minor expansion property",
      "mixing time"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9303M"
    }
  }
}