Browsing by Author "Yin, Jun"
Now showing items 17 of 7

Bulk universality for generalized Wigner matrices
Erdos, Laszlo; Yau, HorngTzer; Yin, Jun (Springer Science + Business Media, 2011)Consider \(N × N\) Hermitian or symmetric random matrices H where the distribution of the (i, j) matrix element is given by a probability measure \(\nu_{ij}\) with a subexponential decay. Let \(\sigma_{ij}^2\) be the ... 
Isotropic local laws for sample covariance and generalized Wigner matrices
Alex, Bloemendal; Erdos, Laszlo; Knowles, Antti; Yau, HorngTzer; Yin, Jun (Institute of Mathematical Statistics, 2014)We consider sample covariance matrices of the form X ∗X, where X is an M × N matrix with independent random entries. We prove the isotropic local MarchenkoPastur law, i.e. we prove that the resolvent (X ∗X − z) −1 converges ... 
Local circular law for random matrices
Bourgade, Paul; Yau, HorngTzer; Yin, Jun (Springer Nature, 2013)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 prove a local version of this law at any point ... 
The local circular law II: the edge case
Bourgade, Paul; Yau, HorngTzer; Yin, Jun (Springer Nature, 2013)In the first part of this article (Bourgade et al. arXiv:1206.1449, 2012), we proved a local version of the circular law up to the finest scale N−1/2+εN−1/2+ε for nonHermitian random matrices at any point z∈ℂz∈C with ... 
A Lower Bound on the Ground State Energy of Dilute Bose Gas
Lee, Ji; Yin, Jun (American Institute of Physics, 2010)Consider an NBoson system interacting via a twobody repulsive shortrange potential \({V}\) in a three dimensional box \({\Lambda}\) of side length \({L}\). We take the limit \({N}\), \({L}\) \({\rightarrow}\) \({\infty}\) ... 
Spectral Statistics of ErdősRényi Graphs II: Eigenvalue Spacing and the Extreme Eigenvalues
Erdos, Laszlo; Knowles, Antti; Yau, HorngTzer; Yin, Jun (Springer Nature, 2012)We consider the ensemble of adjacency matrices of ErdősRényi random graphs, i.e. graphs on N vertices where every edge is chosen independently and with probability p ≡ p(N). We rescale the matrix so that its bulk eigenvalues ...