Partially hyperbolic random dynamics on Grassmannians
Mathematical Physics
2022-11-10 v2 math.MP
Probability
Abstract
A sequence of invertible matrices given by a small random perturbation around a fixed diagonal partially hyperbolic matrix induces a random dynamics on the Grassmann manifolds. Under suitable weak conditions it is known to have a unique invariant (Furstenberg) measure. The main result gives concentration bounds on this measure showing that with high probability the random dynamics stays in the vicinity of stable fixed points of the unperturbed matrix, in a regime where the strength of the random perturbation dominates the local hyperbolicity of the diagonal matrix. As an application, bounds on sums of Lyapunov exponents are obtained.
Cite
@article{arxiv.2206.03444,
title = {Partially hyperbolic random dynamics on Grassmannians},
author = {Joris De Moor and Florian Dorsch and Hermann Schulz-Baldes},
journal= {arXiv preprint arXiv:2206.03444},
year = {2022}
}
Comments
Minor corrections and clarifications on the novelty of the results