Localization-delocalization transitions in random matrix models

Simone Warzel, TU - Munich
Fine Hall 214

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.