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Continuity for random walks in hyperbolic percolation: drift, entropy, and dimension

  • Kohki Sakamoto
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Abstract

For simple random walk on infinite clusters of Bernoulli bond percolation on Cayley graphs of hyperbolic groups, we prove that the drift and asymptotic entropy depend continuously on the percolation parameter throughout the supercritical phase. Together with the dimension formula, this implies continuity of the Hausdorff dimension of harmonic measure on the Gromov boundary.

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Cite

BibTeXRIS
BibTeX
@misc{sakamoto2026continuity,
  title = {{Continuity for random walks in hyperbolic percolation: drift, entropy, and dimension}},
  author = {Kohki Sakamoto},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08519},
  eprint = {2609.08519},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08519},
}
RIS
TY  - UNPB
TI  - Continuity for random walks in hyperbolic percolation: drift, entropy, and dimension
AU  - Kohki Sakamoto
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08519
UR  - https://arxiv.org/abs/2609.08519
AB  - For simple random walk on infinite clusters of Bernoulli bond percolation on Cayley graphs of hyperbolic groups, we prove that the drift and asymptotic entropy depend continuously on the percolation parameter throughout the supercritical phase. Together with the dimension formula, this implies continuity of the Hausdorff dimension of harmonic measure on the Gromov boundary.
ER  -