Mixed random-quasiperiodic cocycles (Q2091203)

The paper starts providing definitions of mixed random quasi-periodic base dynamics, thus characterizing its ergodicity and establishing large deviations estimates for certain observables. Furthermore, the concept of mixed random quasi-periodic cocycle driven by a measure on the group of quasi-periodic cocycles is introduced and discussed. The authors prove that the maximal Lyapunov exponent is upper semicontinuous as a function of the measure with respect to the Wasserstein distance. Then they outline some of the upcoming works on the models introduced here, which mainly focus on the stability under random noise of the Lyapunov exponent of a quasiperiodic cocycle. An important concrete example comes from the study of the Anderson model, which is represented by a discrete random Schrödinger operator used in solid state physics to model one-dimensional disordered systems. In this context, the behavior of the Lyapunov exponent as a function of the energy is directly related to the spectral properties of the Schrödinger operator.