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We generalize Minami's estimate for the Anderson model and its extensions to n eigenvalues, allowing for n arbitrary intervals and arbitrary single-site probability measures with no atoms. As an application, we derive new results about the multiplicity of eigenvalues and Mott's formula for the ac-conductivity when the single site probability distribution is(More)
We investigate the Anderson metal-insulator transition for random Schrödinger operators. We define the strong insulator region to be the part of the spectrum where the random operator exhibits strong dynamical localization in the Hilbert-Schmidt norm. We introduce a local transport exponent β(E), and set the metallic transport region to be the part of the(More)
We prove innnite diierentiability of the magnetization and of all quenched correlation functions for disordered spin systems at high temperature or strong magnetic eld in the presence of Griiths' singularities. We also show uniqueness of the Gibbs state and exponential decay of truncated correlation functions with probability one. Our results are obtained(More)
We consider lattice versions of Maxwell's equations and of the equation that governs the propagation of acoustic waves in a random medium. The vector nature of electromagnetic waves is fully taken into account. The medium is assumed to be a small perturbation of a periodic one. We prove rigorously that localized eigenstates arise in a vicinity of the edges(More)