English

Random walks associated to beta-shifts

Dynamical Systems 2019-10-30 v1

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 β>1\beta>1 that solves βm+1βm1=0\beta^{m+1}-\beta^m-1=0 generalising the work of Fan and Zhu. We also give examples of β\beta where this approach fails.

Keywords

Cite

@article{arxiv.1910.13006,
  title  = {Random walks associated to beta-shifts},
  author = {Bing Li and Yao-Qiang Li and Tuomas Sahlsten},
  journal= {arXiv preprint arXiv:1910.13006},
  year   = {2019}
}
R2 v1 2026-06-23T11:57:49.361Z