Random subshifts of finite type

Mathematics – Probability

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Published in at http://dx.doi.org/10.1214/10-AOP636 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/10-AOP636

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) SFT built from the set $\omega$. For each $0\leq \alpha \leq1$ 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.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Random subshifts of finite type does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Random subshifts of finite type, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random subshifts of finite type will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-367821

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.