Exponential decay of correlations for random interval diffeomorphisms
Dynamical Systems
2026-01-05 v2
Abstract
We consider a finite number of orientation preserving interval diffeomorphisms and apply them randomly in such a way that the expected Lyapunov exponents at the boundary points are positive. We prove the exponential decay of correlations for Lipschitz observables with respect to the unique stationary measure supported on the interior of the interval. The key step is to show the exponential synchronization in average.
Cite
@article{arxiv.2504.16549,
title = {Exponential decay of correlations for random interval diffeomorphisms},
author = {Klaudiusz Czudek},
journal= {arXiv preprint arXiv:2504.16549},
year = {2026}
}
Comments
12 pages, no figures; the title changed from 'Exponential mixing...' to 'Exponential decay of correlations...'. Corollaries have been merged to one, whose formulation now fits the title better. The proof changed accordingly. The main theorem and its proof remain unchanged. The introduction is more detailed now