Strategies in localization proofs for one-dimensional random Schrödinger operators

Abstract

Recent results on localization, both exponential and dynamical, for various models of one-dimensional, continuum, random Schrodinger operators are reviewed. This includes Anderson models with indefinite single site potentials, the BernoulliAnderson model, the Poisson model, and the random displacement model. Among the tools which are used to analyse these models are generalized spectral averaging techniques and results from inverse spectral and scattering theory. A discussion of open problems is included.