The Mobility Edge of Lévy Matrices

Patrick Lopatto,Brown University
Jadwin Hall A06

Lévy matrices are symmetric random matrices whose entry distributions have power law tails and infinite variance. They are predicted to exhibit an Anderson-type phase transition separating a region of delocalized eigenvectors from one with localized eigenvectors. We will discuss the context for this conjecture, and describe a result establishing it when the power law exponent is close to zero or one. This is joint work with Amol Aggarwal and Charles Bordenave.