国（境）外文教专家系列讲座一百七十七讲：加利福尼亚大学河滨分校张正鹤副教授：Positivity and large deviations of the Lyapunov exponents for potentials generated by hyperbolic transformations

发布时间：2023-06-16

一、主讲人介绍：张正鹤副教授

张正鹤，加利福尼亚大学河滨分校 Associate Professor ，主要从事动力系统、谱理论和数学物理方向的研究，本科为中国海洋大学2001级数学系学生，硕士师从南京大学尤建功教授，博士就读于西北大学，师从 Amie Wilkinson 和 Artur Avila ,毕业后曾在莱斯大学从事博士后研究。已在 Invent . Math ., Trans . Amer . Math . Soc ., Comm . Math . Phys ., Int . Math . Res . Not ., J . Funct . Anal ., J . Spectr . Theory 论文。

二、讲座信息

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.

时间：2023年6月27日15:30-16:30

地点：数学院424会议室

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