{
  "id": "1910.07378",
  "version": "v1",
  "published": "2019-10-16T14:38:18.000Z",
  "updated": "2019-10-16T14:38:18.000Z",
  "title": "On Null-homology and stationary sequences",
  "authors": [
    "Gerold Alsmeyer",
    "Chiranjib Mukherjee"
  ],
  "categories": [
    "math.PR",
    "math.DS"
  ],
  "abstract": "The concept of homology, originally developed as a useful tool in algebraic topology, has by now become pervasive in quite different branches of mathematics. The notion particularly carries over quite naturally to the setup of measure-preserving transformations arising from various group actions or, equivalently, the setup of stationary sequences considered in this paper. Our main result provides a sharp criterion which determines (and rules out) when two stationary processes belong to the same {\\it null-homology equivalence class}. We also discuss some concrete cases where the notion of null-homology turns up in a relevant manner.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-16T14:38:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stationary sequences",
      "null-homology equivalence class",
      "stationary processes belong",
      "concrete cases",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}