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arXiv · 2401.05320

Hausdorff dimensions of irreducible Markov hom tree-shifts

Jung-Chao Ban·Guan-Yu Lai·Yu-Liang Wu
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Abstract

This paper features a Cram\'er'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.

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Jung-Chao Ban, Guan-Yu Lai, Yu-Liang Wu. 2024-01-10. Hausdorff dimensions of irreducible Markov hom tree-shifts. https://arxiv.org/abs/2401.05320

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