主讲人：张正鹤 博士（Rice University）

时间：7月7日下午2:30-3:30

地  点：北一区文科楼708教室

摘  要：Positivity and continuity of Lyapunov exponents (LE) play key roles in the spectral analysis of 1D discrete Schrödinger operators, among which the quasiperiodic case is most intensively studied. In 1983, Herman proved that LE is positive for all energies, provided the potentials are trigonometric polynomials. In 1991, Sorets and Spencer showed the similar result for any one-frequency, non-constant real analytic potentials. The positivity and continuity results for multi-frequency case were established by Bourgain, Goldstein, Jitomirskaya and Schlag in early 2000s. All these rely heavily on real analyticity.

In this talk, I will introduce some recent progress concerning the smooth case. Part of these works are joint with Yiqian Wang in which we show uniform positivity and continuity of LE for a class of  quasiperiodic potentials. In particular, the continuity result is the first example in the  category, where . The key estimate is some version of Large Deviation Theorem