Probability and Mathematical Physics Seminar

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The Mobility Edge of Lévy Matrices

Speaker: Patrick Lopatto, Brown University

Location: Warren Weaver Hall 1302

Date: Friday, February 24, 2023, 11:10 a.m.

Synopsis:

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.