Positivity and Large Deviations of the Lyapunov Exponents for Potentials Generated by Hyperbolic Transformations
Time: 2023-05-23
Published By: Wenqiong Li
Speaker(s): Zhenghe Zhang (University of California, Riverside)
Time: 16:00-17:00 June 22, 2023
Venue: Room 9, Quan Zhai, BICMR
In this talk, I will introduce some recent joint work with A. Avila and D. Damanik in showing positivity and large deviations of the Lyapunov exponent for Schrodinger operators with potentials generated by hyperbolic transformations. Specifically, we consider the base dynamics which is a subshift of finite type with an ergodic measure admitting a bounded distortion property and which has a fixed point. We show that if the potentials are locally constant or globally fiber bunched, then the set of zero Lyapunov exponent is finite. Moreover, we have a uniform large deviation estimate away from this finite set. As a consequence, we obtain full spectral Anderson localization for such potentials.
