Mixed random-quasiperiodic cocycles
Ao Cai (PUC-Rio)

Inspired by an intriguing question of Jiangong You on the stability of the Lyapunov exponent of a quasiperiodic Schrödinger cocycle perturbed by a random noise, we started a long-term project called “Mixed Randomquasiperiodic Cocycles”. In this talk, we will introduce the model and talk about our recent progress since 2019, including: ergodic properties, an analog of Furstenberg theory, statistical properties like the large deviation theorem and the central limit theorem, Hölder continuity of the Lyapunov exponent and its stability under random perturbations. This talk is based on a series of joint works with Pedro Duarte (University of Lisbon) and Silvius Klein (PUC-Rio).