Upper bound on the regularity of Lyapunov exponents of random product of matrices

by Jamerson Bezerra (Nicolaus Copernicus University)

Wednesday 29 Mar 2023, 16:00 → 17:00 Europe/Rome

CRM - SNS

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.