Must the Spectrum of a Random Schrödinger Operator Contain an Interval?

We consider Schrödinger operators in $$\ell ^2({\mathbb Z})$$ whose potentials are given by independent (not necessarily identically distributed) random variables. ask whether it is true that almost surely its spectrum contains an interval. provide affirmative answer the case of a sum perturbatively small quasi-periodic potential with analytic sampling function and Diophantine frequency vector term Anderson type, distributed variables (with some small-gap assumption for support single-site distribution). The proof proceeds extending result about presence ground states atypical realizations classical model, which we prove here as well appears to be new.