Lifshits tails in the hierarchical Anderson model

Details Lifshits tails in the hierarchical Anderson model Lifshits tails in the hierarchical Anderson model

2011-01-24

arxiv.org/abs/1101.4468v3

Physics

Mathematical Physics

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

Scientific paper

10.1007/s00023-011-0132-1

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.

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