{
  "id": "1510.05672",
  "version": "v1",
  "published": "2015-10-19T20:22:21.000Z",
  "updated": "2015-10-19T20:22:21.000Z",
  "title": "Nonsingular transformations and dimension spaces",
  "authors": [
    "Thierry Giordano",
    "David Handelman",
    "Radu B. Munteanu"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "For any adic transformation $T$ defined on the path space $X$ of an ordered Bratteli diagram, endowed with a Markov measure $\\mu$, we construct an explicit dimension space (which corresponds to a matrix values random walk on $\\mathbb{Z}$) whose Poisson boundary can be identified as a $\\mathbb{Z}$-space with the dynamical system $(X,\\mu,T)$. We give a couple of examples to show how dimension spaces can be used in the study of nonsingular transformations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-19T20:22:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonsingular transformations",
      "matrix values random walk",
      "explicit dimension space",
      "ordered bratteli diagram",
      "markov measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151005672G"
    }
  }
}