Anderson localization for quasi-one-dimensional disordered models
Hakim Boumaza(Paris Nord)
In this talk I will present the physical phenomenon of Anderson localization and the associated Anderson model for which I will shortly introduce the theory of random operators.
After discussing the known localization results on the Anderson model and the main conjectures which remain unproved, I will focus on one-dimensional and quasi-one-dimensional models. In these cases, the question of Anderson localization reduce to the study of an algebraic object, the Fürstenberg group. The introduction of this group involves typical objects of the dimension one : the transfer matrices, the Lyapunov exponents and a bit of Kotani theory. I will also focus on the properties of the integrated density of states which existence relies on a Feynman-Kac formula.
The talk will end by the presentation of some algebraic tools from Lie group theory which allows to prove the required properties of the Fürstenberg group in different settings.