# Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities

```@article{Lemm2020QuantitativeLB,
title={Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities},
author={Marius Lemm and David Sutter},
journal={Analysis and Mathematical Physics},
year={2020},
volume={12},
pages={1-51}
}```
• Published 24 January 2020
• Mathematics
• Analysis and Mathematical Physics
Lyapunov exponents characterize the asymptotic behavior of long matrix products. In this work we introduce a new technique that yields quantitative lower bounds on the top Lyapunov exponent in terms of an efficiently computable matrix sum in ergodic situations. Our approach rests on two results from matrix analysis—the n -matrix extension of the Golden–Thompson inequality and an effective version of the Avalanche Principle. While applications of this method are currently restricted to uniformly…
2 Citations
• Computer Science, Mathematics
IEEE Transactions on Information Theory
• 2021
An upper and a lower bound are derived for the maximal and minimal Lyapunov exponent, respectively, which assume independence of the random matrices, are analytical, and are tight in the commutative case as well as in other scenarios.
• Mathematics
Random Matrices: Theory and Applications
• 2021
We prove a central limit theorem (CLT) for the product of a class of random singular matrices related to a random Hill’s equation studied by Adams–Bloch–Lagarias. The CLT features an explicit formula

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