题 目： Optimal Large Deviation Theory for analytic quasi periodic Schrödinger cocycle and Hölder regularity of the Lyapunov exponent
时 间: 2018年6月5日 下午16:00-18:00
地 点:蒙民伟楼 1105室
摘 要：We consider 1-d discrete quasi-periodic Schrödinger equations and the associated Schrödinger cocycles. Suppose the potential is real analytic function with bounded extension, assume positive Lyapunov exponents. We prove a refined Large Deviation Theory (LDT) for irrational frequency in the best possible arithmetic regime. The large deviation estimates imply optimal Hölder continuity results of the Lyapunov exponents and the integrated density of states. For small Lyapunov exponent regime, we show that the local Hölder exponent is independent of energy E for Liouville frequency. In the large coupling regime, we show that the local Hölder exponent is independent of the coupling constant. Previously, such coupling independency is only known in the case where the potential is a trigonometric polynomial with Diophantine/Strong Diophantine frequency. This is a joint work with Rui Han at IAS.