Localization for an Anderson-Bernoulli model with generic interaction potential

الأصل · EN

We present a result of localization for a matrix-valued Anderson-Bernoulli operator, acting on L²()⊗ ⁿ, for an arbitrary N≥ 1, whose interaction potential is generic in the real symmetric matrices. For such a generic real symmetric matrix, we construct an explicit interval of energies on which we prove localization, in both spectral and dynamical senses, away from a finite set of critical energies. This construction is based upon the formalism of the Fürstenberg group to which we apply a general criterion of density in semisimple Lie groups. The algebraic nature of the objects we are considering allows us to prove a generic result on the interaction potential and the finiteness of the set of critical energies.