Open Access
Translator Disclaimer
March 2012 Random subshifts of finite type
Kevin McGoff
Ann. Probab. 40(2): 648-694 (March 2012). DOI: 10.1214/10-AOP636

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

Download Citation

Kevin McGoff. "Random subshifts of finite type." Ann. Probab. 40 (2) 648 - 694, March 2012. https://doi.org/10.1214/10-AOP636

Information

Published: March 2012
First available in Project Euclid: 26 March 2012

zbMATH: 1269.37009
MathSciNet: MR2952087
Digital Object Identifier: 10.1214/10-AOP636

Subjects:
Primary: 37B10
Secondary: 37B40 , 60C05

Keywords: Entropy , Random subshifts of finite type

Rights: Copyright © 2012 Institute of Mathematical Statistics

JOURNAL ARTICLE
47 PAGES


SHARE
Vol.40 • No. 2 • March 2012
Back to Top