4 papers
Loop Equations Characterize Random Matrix Statistics
Paul Bourgade, Jiaoyang Huang
We prove that the universal local point processes of random matrix theory are characterized by their loop equation hierarchies. More precisely, for every rational , the $\math…
Fisher-Hartwig asymptotics for non-Hermitian random matrices
Paul Bourgade, Guillaume Dubach, Lisa Hartung +1
We prove the two-dimensional analogue of the asymptotics for Toeplitz determinants with Fisher-Hartwig singularities, for general real symbols. This formula has applications to ran…
Fluctuations for non-Hermitian dynamics
Paul Bourgade, Giorgio Cipolloni, Jiaoyang Huang
We prove that under the Brownian evolution on large non-Hermitian matrices the log-determinant converges in distribution to a 2+1 dimensional Gaussian field in the Edwards-Wilkinso…
Optimal rigidity and maximum of the characteristic polynomial of Wigner matrices
Paul Bourgade, Patrick Lopatto, Ofer Zeitouni
We determine to leading order the maximum of the characteristic polynomial for Wigner matrices and -ensembles. In the special case of Gaussian-divisible Wigner matrices, our met…