The Mobility Edge of Lévy Matrices
CMSA EVENTS: CMSA COLLOQUIUM
When: October 19, 2022
12:45 pm - 1:45 pm
Where: CMSA, 20 Garden St, G10
Address:
20 Garden Street, Cambridge, MA 02138, United States
Speaker: Patrick Lopatto - Brown University
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.