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arXiv · 1910.13006

Random walks associated to beta-shifts

Bing Li·Yao-Qiang Li·Tuomas Sahlsten
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Abstract

We study the dynamics of a simple random walk on subshifts defined by the beta transformation and apply it to find concrete formulae for the Hausdorff dimension of digit frequency sets for $\beta>1$ that solves $\beta^{m+1}-\beta^m-1=0$ generalising the work of Fan and Zhu. We also give examples of $\beta$ where this approach fails.

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Bing Li, Yao-Qiang Li, Tuomas Sahlsten. 2019-10-28. Random walks associated to beta-shifts. https://arxiv.org/abs/1910.13006

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