  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.
