The Mobility Edge of Lévy Matrices

2022-10-19 12:30 - 13:30
CMSA Room G10
Address: CMSA, 20 Garden Street, Cambridge, MA 02138 USA

Colloquium

Speaker: Patrick Lopatto (Brown)

Title: The Mobility Edge of Lévy Matrices

Abstract: Lévy matrices are symmetric random matrices whose entry distributions lie in the domain of attraction of an alpha-stable law; such distributions have infinite variance when alpha is less than 2. Due to the ubiquity of heavy-tailed randomness, these models have been broadly applied in physics, finance, and statistics. When the entries have infinite mean, Lévy matrices are predicted to exhibit a phase transition separating a region of delocalized eigenvectors from one with localized eigenvectors. We will discuss the physical context for this conjecture, and describe a result establishing it for values of alpha close to zero and one. This is joint work with Amol Aggarwal and Charles Bordenave.