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… 

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