December 20, 2004
Alexander Elgart
Title: Moment Analysis for Localization in Random Schroedinger Operators
I will discuss the spectral and dynamical properties of Schroedinger-type operators with random potentials. The new results include a fractional-moment method for continuum operators, which provides exponentially decaying bounds for the mean values of transition amplitudes, and of related resolvent operator kernels, for energies throughout the localization regime. An important component of the analysis is the understanding of the resonance-diffusing effects of the disorder. For the continuum models this is enabled by the use of a result on the boundary-value distribution of resolvents of maximally dissipative operators. This is a joint work with M. Aizenman, S. Naboko, J. Schenker, and G. Stolz.