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Universality of local spectral statistics of random matrices
Laszlo Erdos, Horng-Tzer Yau
The Wigner-Gaudin-Mehta-Dyson conjecture asserts that the local eigenvalue statistics of large random matrices exhibit universal behavior depending only on the symmetry class of th…
Universality of General -Ensembles
Paul Bourgade, Laszlo Erdos, Horng-Tzer Yau
We prove the universality of the -ensembles with convex analytic potentials and for any , i.e. we show that the spacing distributions of log-gases at any inverse temperatur…
Spectral Statistics of Erd{\H o}s-Rényi Graphs II: Eigenvalue Spacing and the Extreme Eigenvalues
Laszlo Erdos, Antti Knowles, Horng-Tzer Yau +1
We consider the ensemble of adjacency matrices of Erd{\H o}s-Rényi random graphs, i.e.\ graphs on vertices where every edge is chosen independently and with probability $p \equ…
Spectral statistics of Erdős-Rényi graphs I: Local semicircle law
László Erdős, Antti Knowles, Horng-Tzer Yau +1
We consider the ensemble of adjacency matrices of Erdős-Rényi random graphs, that is, graphs on vertices where every edge is chosen independently and with probability $p\equiv…