Hausdorff dimensions of irreducible Markov hom tree-shifts

Jung Chao Ban; Guan Yu Lai; Yu Liang Wu

doi:10.1112/jlms.70198

Hausdorff dimensions of irreducible Markov hom tree-shifts

Jung Chao Ban
, Guan Yu Lai
, Yu Liang Wu^*

^*Corresponding author for this work

Research output: Contribution to journal › Journal Article › peer-review

Abstract

This paper features a Cramér's theorem for finite-state Markov chains indexed by rooted (Formula presented.) -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.

Original language	English
Article number	e70198
Journal	Journal of the London Mathematical Society
Volume	111
Issue number	6
DOIs	https://doi.org/10.1112/jlms.70198
State	Published - 06 2025
Externally published	Yes

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© 2025 The Author(s). The Journal of the London Mathematical Society is copyright © London Mathematical Society.

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10.1112/jlms.70198

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title = "Hausdorff dimensions of irreducible Markov hom tree-shifts",

abstract = "This paper features a Cram{\'e}r's theorem for finite-state Markov chains indexed by rooted (Formula presented.) -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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AB - This paper features a Cramér's theorem for finite-state Markov chains indexed by rooted (Formula presented.) -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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DO - 10.1112/jlms.70198

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JO - Journal of the London Mathematical Society

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Hausdorff dimensions of irreducible Markov hom tree-shifts

Abstract

Bibliographical note

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