Finite Orbits in Random Subshifts of Finite Type

• Ryan Broderick ^[1]
  1. [1] University of California (USA)
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 16, Nº 3, 2017, págs. 531-545
• Idioma: inglés
• DOI: 10.1007/s12346-017-0224-5
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• Resumen

  • For each n, d ∈ N and 0 <α< 1, we define a random subset of A{1,2,...,n}d by independently including each element with probability α and excluding it with probability 1−α, and consider the associated random subshift of finite type. Extending results of McGoff (Ann Probab 40(2):648–694, 2012) and of McGoff and Pavlov (arxiv:1408.4086), we prove there exists α0 = α0(d, |A|) > 0 such that for α<α0 and with probability tending to 1 as n → ∞, this random subshift will contain only finitely many elements. In the case d = 1, we obtain the best possible such α0, 1/|A|.