{
  "id": "2208.05239",
  "version": "v1",
  "published": "2022-08-10T09:37:19.000Z",
  "updated": "2022-08-10T09:37:19.000Z",
  "title": "Poincaré inequalities for Markov chains: a meeting with Cheeger, Lyapunov and Metropolis",
  "authors": [
    "Christophe Andrieu",
    "Anthony Lee",
    "Sam Power",
    "Andi Q. Wang"
  ],
  "comment": "80 pages",
  "categories": [
    "math.PR",
    "stat.CO"
  ],
  "abstract": "We develop a theory of weak Poincar\\'e inequalities to characterize convergence rates of ergodic Markov chains. Motivated by the application of Markov chains in the context of algorithms, we develop a relevant set of tools which enable the practical study of convergence rates in the setting of Markov chain Monte Carlo methods, but also well beyond.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-10T09:37:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J22",
      "65C05"
    ],
    "keywords": [
      "markov chain monte carlo methods",
      "metropolis",
      "weak poincare inequalities",
      "ergodic markov chains",
      "characterize convergence rates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 80,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}