Abstract
We present a result of localization for a matrix-valued Anderson-Bernoulli operator acting on the space of $\boldsymbol{C}^N$-valued square-integrable functions, for an arbitrary $N$ larger than 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.
Citation
Hakim Boumaza. "Localization for an Anderson-Bernoulli model with generic interaction potential." Tohoku Math. J. (2) 65 (1) 57 - 74, 2013. https://doi.org/10.2748/tmj/1365452625
Information