PreprintarXiv licencearXiv
Absolute continuity of invariant measures for random diffeomorphisms
Abstract
We develop criteria showing that invariant measures for random walks generated by diffeomorphisms of manifolds are in the Lebesgue class. Our assumptions are first, that there is a uniform expansion gap in the Lyapunov spectrum of the random walk, and second, that the conditionals of the invariant measure along the appropriate (partial) stable manifolds are in the Lebesgue class.
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BibTeX
@misc{brown2026absolute,
title = {{Absolute continuity of invariant measures for random diffeomorphisms}},
author = {Aaron Brown and Alex Eskin and Simion Filip and Federico Rodriguez Hertz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22654},
eprint = {2610.22654},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22654},
}
RIS
TY - UNPB
TI - Absolute continuity of invariant measures for random diffeomorphisms
AU - Aaron Brown
AU - Alex Eskin
AU - Simion Filip
AU - Federico Rodriguez Hertz
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22654
UR - https://arxiv.org/abs/2610.22654
AB - We develop criteria showing that invariant measures for random walks generated by diffeomorphisms of manifolds are in the Lebesgue class. Our assumptions are first, that there is a uniform expansion gap in the Lyapunov spectrum of the random walk, and second, that the conditionals of the invariant measure along the appropriate (partial) stable manifolds are in the Lebesgue class.
ER -