{
  "id": "1912.10715",
  "version": "v1",
  "published": "2019-12-23T10:21:41.000Z",
  "updated": "2019-12-23T10:21:41.000Z",
  "title": "Analysis of non-reversible Markov chains via similarity orbit",
  "authors": [
    "Michael C. H. Choi",
    "Pierre Patie"
  ],
  "comment": "29 pages. To appear in Combin. Probab. Comput",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we develop an in-depth analysis of non-reversible Markov chains on denumerable state space from a similarity orbit perspective. In particular, we study the class of Markov chains whose transition kernel is in the similarity orbit of a normal transition kernel, such as the one of birth-death chains or reversible Markov chains. We start by identifying a set of sufficient conditions for a Markov chain to belong to the similarity orbit of a birth-death one. As by-products, we obtain a spectral representation in terms of non-self-adjoint resolutions of identity in the sense of Dunford [21] and offer a detailed analysis on the convergence rate, separation cutoff and ${\\rm{L}}^2$-cutoff of this class of non-reversible Markov chains. We also look into the problem of estimating the integral functionals from discrete observations for this class. In the last part of this paper, we investigate a particular similarity orbit of reversible Markov kernels, that we call the pure birth orbit, and analyze various possibly non-reversible variants of classical birth-death processes in this orbit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-23T10:21:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J05",
      "60J10",
      "60J27"
    ],
    "keywords": [
      "non-reversible markov chains",
      "similarity orbit",
      "pure birth orbit",
      "birth-death",
      "normal transition kernel"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}