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Ergodicity of (co)expanding on average random dynamical systems
Abstract
We prove ergodicity for random dynamics satisfying some expansion and irreducibility conditions. As a particular application, we show that if R1,R2∈ SO(d+1), d≥ 2, generate a dense subgroup, then the random dynamics of R1 and R2 on Sd is stably ergodic. Previously this was only known to hold in even dimensions. As a consequence, we deduce spectral gap and statistical limit theorems for such systems. In particular, our results apply in the presence of zero Lyapunov exponents.
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BibTeX
@misc{dewitt2026ergodicity,
title = {{Ergodicity of (co)expanding on average random dynamical systems}},
author = {Jonathan DeWitt and Dmitry Dolgopyat and Zhiyuan Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.21199},
eprint = {2605.21199},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.21199},
}
RIS
TY - UNPB
TI - Ergodicity of (co)expanding on average random dynamical systems
AU - Jonathan DeWitt
AU - Dmitry Dolgopyat
AU - Zhiyuan Zhang
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2605.21199
UR - https://arxiv.org/abs/2605.21199
AB - We prove ergodicity for random dynamics satisfying some expansion and irreducibility conditions. As a particular application, we show that if R_1,R_2∈ SO(d+1), d≥ 2, generate a dense subgroup, then the random dynamics of R_1 and R_2 on S^d is stably ergodic. Previously this was only known to hold in even dimensions. As a consequence, we deduce spectral gap and statistical limit theorems for such systems. In particular, our results apply in the presence of zero Lyapunov exponents.
ER -