Dynamical Systems Seminar
# Upper bound on the regularity of Lyapunov exponents of random product of matrices

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Europe/Rome

CRM - SNS
#### CRM - SNS

Description

The study of the regularity of the Lyapunov exponent of random products of SL2(R) matrices is a rich subject with many important contributions in the past years. It is well established in the literature that the function which associates each finite supported measure $\mu$ its Lyapunov exponents $L(\mu)$ is continuous, however, in general, it can have really poor modulus of continuity.

The purpose of this talk is to present a quantitative result on the control of the modulus of continuity for generic finitely supported measures $\mu$. More specifically, we provide an explicit upper bound on the local Holder regularity of the Lyapunov for this generic class.