Lifshits tails in the hierarchical Anderson model

Abstract

We prove that the homogeneous hierarchical Anderson model exhibits a Lifshits tail at the upper edge of its spectrum. The Lifshits exponent is given in terms of the spectral dimension of the homogeneous hierarchical structure. Our approach is based on Dirichlet-Neumann bracketing for the hierarchical Laplacian and a large-deviation argument.

17 pages, 1 figure; changes in v2: references added, typos corrected; changes in v3: Lemma 3.3 slightly corrected; to appear in Ann. Henri Poincare

References in corpus (2)

• Poisson statistics of eigenvalues in the hierarchical Anderson model
• Equality of Lifshitz and van Hove exponents on amenable Cayley graphs

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