@inbook{0e2efdab99ea4bf6b50135a56bc726f2,
title = "Singular spectrum and recent results on hierarchical operators",
abstract = "We use trace class scattering theory to exclude the possibility of absolutely continuous spectrum in a large class of self-adjoint operators with an underlying hierarchical structure and provide applications to certain random hierarchical operators and matrices. We proceed to contrast the localizing effect of the hierarchical structure in the deterministic setting with previous results and conjectures in the random setting. Furthermore, we survey stronger localization statements truly exploiting the disorder for the hierarchical Anderson model and report recent results concerning the spectral statistics of the ultrametric random matrix ensemble.",
keywords = "Absolutely continuous spectrum, Hierarchical operators, Localization",
author = "{von Soosten}, Per and Simone Warzel",
note = "Publisher Copyright: {\textcopyright} 2017 Per von Soosten and Simone Warzel.",
year = "2018",
doi = "10.1090/conm/717/14450",
language = "English",
series = "Contemporary Mathematics",
publisher = "American Mathematical Society",
pages = "215--225",
booktitle = "Contemporary Mathematics",
}