Hausdorff dimensions of topologically transitive Markov hom tree-shifts

Abstract

This paper features an analog of Sanov's theorem for finite-state Markov chains indexed by rooted d-trees, obtained via the method of types in the classical analysis of large deviations. Along with the theorem comes two applications: an almost-sure type convergence of sample means and a formula for the Hausdorff dimension of the symbolic space associated with the irreducible Markov chain.