Abstract.
We study the eigenvalue statistics for the hieracharchial Anderson model of Molchanov [21–23,27,28]. We prove Poisson fluctuations at arbitrary disorder, when the the model has a spectral dimension d < 1. The proof is based on Minami’s technique [25] and we give an elementary exposition of the probabilistic arguments.
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Communicated by Claude-Alain Pillet.
Submitted: October 8, 2007. Accepted: December 17, 2007.
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Kritchevski, E. Poisson Statistics of Eigenvalues in the Hierarchical Anderson Model. Ann. Henri Poincaré 9, 685–709 (2008). https://doi.org/10.1007/s00023-008-0369-5
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DOI: https://doi.org/10.1007/s00023-008-0369-5