  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].
