Subshifts of finite type with a hole

We consider a subshift of finite type on q symbols with a union of t cylinders based at words of identical length p as the hole. We explore the relationship between the escape rate into the hole and a rational function, $r(z)$ , of correlations between forbidden words in the subshift with the hole. In particular, we prove that there exists a constant $D(t,p)$ such that if $q>D(t,p)$ , then the escape rate is faster into the hole when the value of the corresponding rational function $r(z)$ evaluated at $D(t,p)$ is larger. Further, we consider holes which are unions of cylinders based at words of identical length, having zero cross-correlations, and prove that the escape rate is faster into the hole with larger Poincaré recurrence time. Our results are more general than the existing ones known for maps conjugate to a full shift with a single cylinder as the hole.