Positivity and Large Deviations of the Lyapunov Exponents for Potentials Generated by Hyperbolic Transformations
发布时间：2023年05月23日
浏览次数：2519
发布者: Wenqiong Li
主讲人： 张正鹤（加利福尼亚大学河滨分校）
活动时间： 从 2023-06-22 16:00 到 17:00
场地： 北京国际数学研究中心，全斋全9教室
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.
