Consider a discrete, quasi-periodic Schrodinger operator with analytic potential. We show that the corresponding Lyapunov exponent is stable under small random perturbations of the potential, provided that the random noise satisfies an appropriate regularity condition. This answers positively a question posed to the authors by Jiangong You. I will describe various other projects motivated by this question.

Joint work with Ao Cai (Soochow University) and Pedro Duarte (Lisbon University).