RANDOM SUBSHIFTS OF FINITE TYPE

• 成果类型: Article
• 署名作者: McGoff, Kevin
• 署名单位: University System of Maryland; University of Maryland College Park
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP636
• 发表日期: 2012
• 页码: 648-694
• 关键词: conditionally invariant-measures; markov extensions; unavoidable sets; anosov maps; entropy; graphs; holes

摘要

Let X be an irreducible shift of finite type (SFT) of positive entropy, and let B-n(X) be its set of words of length n. Define a random subset omega of B-n(X) by independently choosing each word from B-n(X) with some probability alpha. Let X-omega be the (random) SET built from the set omega. For each 0 <= alpha <= 1 and n tending to infinity, we compute the limit of the likelihood that X-omega is empty, as well as the limiting distribution of entropy for X-omega. For alpha near 1 and n tending to infinity, we show that the likelihood that X-omega contains a unique irreducible component of positive entropy converges exponentially to 1. These results are obtained by studying certain sequences of random directed graphs. This version of random SFT differs significantly from a previous notion by the same name, which has appeared in the context of random dynamical systems and bundled dynamical systems.