Limit-periodic Schrodinger operators on Zd: Uniform localization

We exhibit d-dimensional limit-periodic Schrodinger operators that are uniformly localized in the strongest sense possible. That is, for each of these operators, there is a uniform exponential decay rate such that every element of the hull of the corresponding Schrodinger operator has a complete set of eigen-vectors that decay exponentially off their centers of localization at least as fast as prescribed by the uniform decay rate. Consequently, these operators exhibit uniform dynamical localization. (C) 2013 Elsevier Inc. All rights reserved.