Abstract
Let X be an irreducible shift of finite type (SFT) of positive entropy, and let Bn(X) be its set of words of length n. Define a random subset ω of Bn(X) by independently choosing each word from Bn(X) with some probability α. Let Xω be the (random) SFT built from the set ω. For each 0 ≤ α ≤ 1 and n tending to infinity, we compute the limit of the likelihood that Xω is empty, as well as the limiting distribution of entropy for Xω. For α near 1 and n tending to infinity, we show that the likelihood that Xω 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.
Citation
Kevin McGoff. "Random subshifts of finite type." Ann. Probab. 40 (2) 648 - 694, March 2012. https://doi.org/10.1214/10-AOP636
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