{
  "id": "1506.02600",
  "version": "v1",
  "published": "2015-06-08T17:54:33.000Z",
  "updated": "2015-06-08T17:54:33.000Z",
  "title": "Finite orbits in random subshifts of finite type",
  "authors": [
    "Ryan Broderick"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "For each $n, d \\in \\mathbb{N}$ and $0 < \\alpha < 1$, we define a random subset of $\\mathcal{A}^{\\{1, 2, \\dots, n\\}^d}$ by independently including each element with probability $\\alpha$ and excluding it with probability $1-\\alpha$, and consider the associated random subshift of finite type. Extending results of McGoff and of McGoff and Pavlov, we prove there exists $\\alpha_0 = \\alpha(d, |\\mathcal{A}|) > 0$ such that for $\\alpha < \\alpha_0$ and with probability tending to $1$ as $n \\to \\infty$, this random subshift will contain only finitely many elements. In the case $d = 1$, we obtain the best possible such $\\alpha_0$, $1/|\\mathcal{A}|$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-08T17:54:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite type",
      "finite orbits",
      "probability",
      "associated random subshift",
      "random subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150602600B"
    }
  }
}