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arXiv · 1811.10517

Delocalization and continuous spectrum for ultrametric random operators

Per von Soosten·Simone Warzel
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Abstract

This paper studies the delocalized regime of an ultrametric random operator whose independent entries have variances decaying in a suitable hierarchical metric on $\mathbb{N}$. When the decay-rate of the off-diagonal variances is sufficiently slow, we prove that the spectral measures are uniformly $\theta$-H\"{o}lder continuous for all $\theta \in (0,1)$. In finite volumes, we prove that the corresponding ultrametric random matrices have completely extended eigenfunctions and that the local eigenvalue statistics converge in the Wigner-Dyson-Mehta universality class.

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Per von Soosten, Simone Warzel. 2018-11-26. Delocalization and continuous spectrum for ultrametric random operators. https://doi.org/10.1007/s00023-019-00809-z

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