Entropy along convex shapes, random tilings and shifts of finite type
Entropy along convex shapes, random tilings and shifts of finite type
A well-known formula for the topological entropy of a symbolic system is $h_{\operatorname{top}}(X)=\lim_{n\to\infty} \log N(\Lambda_n)/|\Lambda_n|$, where $\Lambda_n$ is the box of side $n$ in $\mathbb{Z}^d$ and $N(\Lambda)$ is the number of configurations of the system on the finite subset $\Lambda$ of $\mathbb{Z}^d$. We investigate the convergence of the above limit …