{
  "id": "1705.00042",
  "version": "v1",
  "published": "2017-04-28T19:12:15.000Z",
  "updated": "2017-04-28T19:12:15.000Z",
  "title": "Factor maps and embeddings for random $\\mathbb{Z}^d$ shifts of finite type",
  "authors": [
    "Kevin McGoff",
    "Ronnie Pavlov"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "For any $d \\geq 1$, random $\\mathbb{Z}^d$ shifts of finite type (SFTs) were defined in previous work of the authors. For a parameter $\\alpha \\in [0,1]$, an alphabet $\\mathcal{A}$, and a scale $n \\in \\mathbb{N}$, one obtains a distribution of random $\\mathbb{Z}^d$ SFTs by randomly and independently forbidding each pattern of shape $\\{1,\\dots,n\\}^d$ with probability $1-\\alpha$ from the full shift on $\\mathcal{A}$. We prove two main results concerning random $\\mathbb{Z}^d$ SFTs. First, we establish sufficient conditions on $\\alpha$, $\\mathcal{A}$, and a $\\mathbb{Z}^d$ subshift $Y$ so that a random $\\mathbb{Z}^d$ SFT factors onto $Y$ with probability tending to one as $n$ tends to infinity. Second, we provide sufficient conditions on $\\alpha$, $\\mathcal{A}$ and a $\\mathbb{Z}^d$ subshift $X$ so that $X$ embeds into a random $\\mathbb{Z}^d$ SFT with probability tending to one as $n$ tends to infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-28T19:12:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite type",
      "factor maps",
      "embeddings",
      "main results concerning random",
      "full shift"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}