Monday, October 28, 2019 at 4:15pm to 5:15pm
Room : 2 - 147 182 memorial Drive, MIT Building 2, Cambridge, MA, 02142
Featured Speaker : Patrick Lopatto (Harvard University, Department of Mathematics)
Title : Spectral Statistics of Lévy matrices
Lvy matrices are symmetric random matrices whose entries are independent \alpha-stable laws. Such distributions have infinite variance, and when \alpha< 1, infinite mean. In the latter case, these matrices are conjectured to exhibit a sharp transition from a delocalized regime at low energy to a localized regime at high energy, like the infamous Anderson model in mathemat- ical physics. We discuss work establishing the existence of a delocalized regime with GOE eigenvalue statistics. Further, we characterize the eigenvector statistics in this regime and find they display novel, non-Gaussian behavior.
These describe joint works with Amol Aggarwal, Jake Marcinek, and Horng-Tzer Yau.