Work

Absolute continuity of invariant measures for random diffeomorphisms

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.22654

Authors: Brown, Aaron, Eskin, Alex, Filip, Simion, Hertz, Federico Rodriguez

Institution: University of Chicago

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7222919036

Cites: 3

Cited by:

Related to: 10