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Fluctuation based proof of the stability of ac spectra of random operators on tree graphs

Michael Aizenman·Robert Sims·Simone Warzel
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Abstract

We summarize recent works on the stability under disorder of the absolutely continuous spectra of random operators on tree graphs. The cases covered include: Schrödinger operators with random potential, quantum graph operators for trees with randomized edge lengths, and radial quasi-periodic operators perturbed by random potentials.

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Michael Aizenman, Robert Sims, Simone Warzel. 2005-10-18. Fluctuation based proof of the stability of ac spectra of random operators on tree graphs. https://arxiv.org/abs/math-ph/0510069

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