On the Kunz-Souillard approach to localization for the discrete one dimensional generalized Anderson model

Understand

We prove dynamical and spectral localization at all energies for the discrete generalized Anderson model via the Kunz-Souillard approach to localization.

• This is an extension of the original Kunz-Souillard approach to localization for Schr\"odinger operators, to the case where a single random variable determines the potential on a block of an arbitrary, but fixed, size $\alpha$.
• For this model, we also give a description of the almost sure spectrum as a set and prove uniform positivity of the Lyapunov exponents.
• In fact, regarding positivity of the Lyapunov exponents, we prove a stronger statement where we also allow finitely supported distributions.