Resonant delocalization on the Bethe strip

Abstract

Recently, Aizenman and Warzel discovered a mechanism for the appearance of absolutely continuous spectrum for random Schroedinger operators on the Bethe lattice through rare resonances (resonant delocalization). We extend their analysis to operators with matrix-valued random potentials drawn from ensembles such as the Gaussian Orthogonal Ensemble. These operators can be viewed as random operators on the Bethe strip, a graph (lattice) with loops.

24 pages; fixed some typos

References in corpus (2)

• Localisation for non-monotone Schroedinger operators
• Surprises in the phase diagram of the Anderson model on the Bethe lattice

Cited by in corpus (5)

• Anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channel
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• Absolutely Continuous Spectrum for random Schroedinger operators on the Fibonacci and similar tree-strips
• A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes
• Random Schrödinger Operators on discrete structures