Random and mean Lyapunov exponents for $\mathrm{GL}_n(\mathbb{R})$
Dynamical Systems
2022-08-23 v3 Mathematical Physics
math.MP
Representation Theory
Abstract
We consider orthogonally invariant probability measures on and compare the mean of the logs of the moduli of eigenvalues of the matrices to the Lyapunov exponents of random matrix products independently drawn with respect to the measure. We give a lower bound for the former in terms of the latter. The results are motivated by Dedieu-Shub\cite{DS}. A novel feature of our treatment is the use of the theory of spherical polynomials in the proof of our main result.
Cite
@article{arxiv.2206.01091,
title = {Random and mean Lyapunov exponents for $\mathrm{GL}_n(\mathbb{R})$},
author = {Diego Armentano and Gautam Chinta and Siddhartha Sahi and Michael Shub},
journal= {arXiv preprint arXiv:2206.01091},
year = {2022}
}