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The Localization Transition in the Ultrametric Ensemble by von Soosten, Per; Warzel, Simone is a scholarly article available to read on EtoBox.

What is The Localization Transition in the Ultrametric Ensemble about?

We study the hierarchical analogue of power-law random band matrices, a symmetric ensemble of random matrices with independent entries whose variances decay exponentially in the metric induced by the tree topology on $\mathbb{N}$. We map out the entirety of the localization regime by proving the localization of eigenfunctions and Poisson statistics of the suitably scaled eigenvalues. Our results complement existing works on complete delocalization and random matrix universality, thereby proving the existence of a phase transition in this model.

Author

von Soosten, Per; Warzel, Simone

Published

2017

Language

EN