On the topological pressure of axial product on trees

Jung-Chao Ban; Yu-Liang Wu

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arXiv · 2310.10242

On the topological pressure of axial product on trees

Jung-Chao Ban·Yu-Liang Wu

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Abstract

This article investigates the topological pressure of isotropic axial products of Markov subshifts on the $d$-tree. We show that the quantity increases with dimension $d$. To achieve this, we introduce the pattern distribution vectors and the associated transition matrices and partially transplant the large deviation theory to tree-shifts. Additionally, we apply our main result to a broader class of shift spaces, accompanied by numerical experiments for verification.

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Jung-Chao Ban, Yu-Liang Wu. 2023-10-16. On the topological pressure of axial product on trees. https://arxiv.org/abs/2310.10242

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