On non-perturbative Anderson localization for Cα potentials generated by shifts and skew-shifts
Abstract
In this paper we address the question of proving Anderson localization (AL) for the operator [H(x,ω)](n) := - (n+1) - (n-1) + V(Tnω x)(n), n∈ Z where T:22 is either the shift or the skew-shift and V is only Cα(2) for some α>0. We show that under the assumption of positive Lyapunov exponents, (AL) takes place for a.e. frequency, phase, and energy.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.