Wed, May 9, 2018, 3:00 pm

Location:

214 Jadwin Hall

Speaker(s):

Simone Warzel

TU Munich

Abstract: Hermitian random matrix models are known to exhibit phase transitions regarding both their local eigenvalue statistics and in the eigenvectors’ localisation properties. The poster child of such is the Rosenzweig-Porter model, which is based on the interpolation between a random diagonal matrix and GOE. Interestingly, this model has recently been shown to exhibit a phase in which the eigenvectors exhibit non-ergodic delocalisation alongside local GOE statistics. In this talk, I will explain the main ideas behind the emergence of this phase. I will also address the motivation of these questions and consequences for the ultra-metric ensemble.