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Localization and delocalization for ultrametric random matrices

Mathematical Physics & Probability

Speaker: Per von Soosten, Harvard University
Related Webpage: http://people.math.harvard.edu/~vonsoosten/
Location: Zoom (online)
Start time: Wed, May 27 2020, 2:10PM

We consider a Dyson-hierarchical analogue of power-law random band matrices with Gaussian entries. The model can be constructed recursively by alternating between averaging independent copies of the matrix and running Dyson Brownian motion. We use this to map out the localized regime and a large part of the delocalized regime in terms of local statistics and eigenfunction decay. Our method extends to a part of the delocalized regime in which the model has a well-defined infinite-volume limit with Holder-continuous spectral measures. This talk is based on joint work with Simone Warzel.