Frederic Klopp
Weak disorder localization and Lifshitz tails
(393K, Postscript)

ABSTRACT.   This paper is devoted to the study of localization of discrete 
 random Schr dinger Hamiltonians in the weak disorder regime. 
 Consider an i.i.d. Anderson model and assume that its left spectral 
 edge is 0. Let $\gamma$ be the coupling constant measuring the 
 strength of the disorder. For $\gamma$ small, we prove a Lifshitz 
 tail type estimate and use it to derive localization in a band 
 starting at 0 going up to a distance $\gamma^{1+\eta}$ 
 ($0<\eta<\eta_0$) of the average of the potential. In this energy 
 region, we show that the localization length at energy $E$ is 
 bounded from above by a constant times the square root of the 
 distance between $E$ and the average of the potential.