Hausdorff dimensions of irreducible Markov hom tree‐shifts
Ban, Jung‐Chao; Lai, Guan‐Yu; Wu, Yu‐Liang (2025-06-05)
London mathematical society
05.06.2025
Ban, J.-C., Lai, G.-Y. and Wu, Y.-L. (2025), Hausdorff dimensions of irreducible Markov hom tree-shifts. J. London Math. Soc., 111: e70198. https://doi.org/10.1112/jlms.70198
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© 2025 The Author(s). The Journal of the London Mathematical Society is copyright © London Mathematical Society. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
https://creativecommons.org/licenses/by/4.0/
© 2025 The Author(s). The Journal of the London Mathematical Society is copyright © London Mathematical Society. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
https://creativecommons.org/licenses/by/4.0/
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-202506184734
https://urn.fi/URN:NBN:fi:oulu-202506184734
Tiivistelmä
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.
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.
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