Hausdorff dimensions of irreducible Markov hom tree-shifts

2024/01/10 by Jung‐Chao Ban, Ban, Jung-Chao, Guan‐Yu Lai +3 · 1 citation
Mathematics · #28A80 #60J10 (Primary) 37B10 (Secondary) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2401.05320

openalex publication_date 2024/01/10 · openalex created_date 2024/01/13 · openalex updated_date 2026/07/28

Abstract

This paper features a Cramér'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.

Cited by

• One-sided Hom shifts

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