Joint IAS/PU Analysis and Mathematical Physics

I will talk about joint work with my student Reuben Drogin.  We prove delocalization for the homogeneous Anderson model on an infinite regular tree (or Caley graph or Bethe lattice) with small bounded disorder. This extends earlier results of Klein and Aizenman--Warzel by covering the previously missing parts of the spectrum. Our argument generalizes to any disorder with a finite fourth moment and a sub-Cauchy density.  We prove continuity of the Lyapunov exponent as the disorder vanishes.