# 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} }

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

### Bounds on Lyapunov Exponents via Entropy Accumulation

- Computer Science, MathematicsIEEE 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.

### CLT with explicit variance for products of random singular matrices related to Hill’s equation

- MathematicsRandom 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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