06-123 Kritchevski, E.

Hierarchical Anderson Model (43K, LaTeX 2e) Apr 22, 06

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Abstract. In this article, we will review the spectral localization problem in the hierarchical Anderson model. We will present the original result of Molchanov on localization at arbitrary disorder in any spectral dimension, when the random perturbations are i.i.d. with a Cauchy distribution, as well as generalization to the case of mixed Cauchy distributions. We will also prove the new result that in spectral dimension $\rm{d}\leq 4$, localization holds for very general distributions of the perturbation.

Files: 06-123.src( 06-123.keywords , HierarchicalReview.tex )