A "random" shift of finite type over an alphabet A was defined by Kevin
McGoff as follows: for any \(t\) in \([0,1]\) and positive integer \(n\),
define a "random" set of words \(S\) which independently contains each
possible word of length \(n\) with probability \(t\) (or omits it, with
probability \(1-t)\). This defines a "random" shift of finite type \(X\)
over \(A\) where \(S\) is the allowed set of \(n\)-letter words.
Fixing \(A\) and \(t\) and letting \(n\) approach infinity, he proved
several interesting results about aspects of random shifts of finite type
in the limit, such as the probability that \(X\) is empty and the
topological entropy of \(X\).
I will present current joint work with Kevin in which we extend several of
his results to \(\mathbb{Z}^d\) shifts of finite type. I'll also describe
some of the fundamental differences between shifts of finite type in
\(\mathbb{Z}\) and \(\mathbb{Z}^d\), and implications of our results in
that context.
I'll assume some familiarity with one-dimensional shifts of finite type and
basic dynamical notions such as periodic points and topological entropy,
but most definitions will be briefly reviewed regardless.
Webmaster University of Houston
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Last modified: April 08 2016 - 20:30:35
