Speaker
Charles Bordenave
Description
This is an ongoing joint work with Alice Guionnet and Camille Male. We
consider a finite collection of Hermitian heavy-tailed random matrices
of dimension N. Our model include the Lévy matrices introduced by
Bouchaud and Cizeau or sparse random matrices with O(1) non-zeroes
entries per row. When represented as weighted graphs on N vertices,
these matrices have local weak limits in the Benjamini-Schramm topology.
Thanks to this representation, we establish large deviations principle
for macroscopic observables of such collection of matrices. These
observable include the empirical distribution of the eigenvalues and
empirical distribution of the neighborhood distribution.