PreprintCC BY-SA 4.0arXiv
Continuity of Furstenberg entropy on Bowen Poisson bundles
Abstract
We provide a sufficient criterion for continuity of the Furstenberg entropy of Bowen Poisson bundles, jointly in the random walk measure and the underlying invariant random subgroup. The criterion applies in particular for tree-like Poisson bundles of a free group and for intersectional invariant random subgroups on lamplighter groups. It also provides continuity of the boundary entropy spectrum of powers of prime measured groups.
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BibTeX
@misc{brieussel2026continuity,
title = {{Continuity of Furstenberg entropy on Bowen Poisson bundles}},
author = {Jérémie Brieussel and Hanna Oppelmayer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29561},
eprint = {2610.29561},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29561},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Continuity of Furstenberg entropy on Bowen Poisson bundles
AU - Jérémie Brieussel
AU - Hanna Oppelmayer
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29561
UR - https://arxiv.org/abs/2610.29561
AB - We provide a sufficient criterion for continuity of the Furstenberg entropy of Bowen Poisson bundles, jointly in the random walk measure and the underlying invariant random subgroup. The criterion applies in particular for tree-like Poisson bundles of a free group and for intersectional invariant random subgroups on lamplighter groups. It also provides continuity of the boundary entropy spectrum of powers of prime measured groups.
ER -