152 citations · 743 across the 29 of their papers we have counts for
4 papers · 1 filter
The local circular law II: the edge case
Paul Bourgade, Horng-Tzer Yau, Jun Yin
In the first part of this article, we proved a local version of the circular law up to the finest scale $N^{-1/2+ \e}$ for non-Hermitian random matrices at any point $z \in \C$ wit…
Local Circular Law for Random Matrices
Paul Bourgade, Horng-Tzer Yau, Jun Yin
The circular law asserts that the spectral measure of eigenvalues of rescaled random matrices without symmetry assumption converges to the uniform measure on the unit disk. We prov…
Strong Szego asymptotics and zeros of the zeta function
Paul Bourgade, Jeffrey Kuan
Assuming the Riemann hypothesis, we prove the weak convergence of linear statistics of the zeros of L-functions towards a Gaussian field, with covariance structure corresponding to…
Bulk Universality of General -Ensembles with Non-convex Potential
Paul Bourgade, Laszlo Erdos, Horng-Tzer Yau
We prove the bulk universality of the -ensembles with non-convex regular analytic potentials for any . This removes the convexity assumption appeared in our earlier work. T…