Multi-Scale Jacobi Method for Anderson Localization
  A new KAM-style proof of Anderson localization is obtained. A sequence of local rotations is defined, such that off-diagonal matrix elements of the Hamiltonian are driven rapidly to zero. This leads to the first proof via multi-scale analysis of exponential decay of the eigenfunction correlator (this implies strong dynamical localization). The method has been used in recent work on many-body localization [arXiv:1403.7837]. 
John Z. Imbrie
math-ph cond-mat.dis-nn math.MP math.PR