Singular spectrum and recent results on hierarchical operators

Per von Soosten, Simone Warzel

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

2 Scopus citations


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.

Original languageEnglish
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Number of pages11
StatePublished - 2018

Publication series

NameContemporary Mathematics
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627


  • Absolutely continuous spectrum
  • Hierarchical operators
  • Localization


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