Z. Bao

activity

20112021

most citedDelocalization for a class of random block band matrices

6 citations · 10 across the 4 of their papers we have counts for

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6 papers · 1 filter

math.PR2021★ 4 cited

Quantitative CLT for linear eigenvalue statistics of Wigner matrices

Zhigang Bao, Yukun He

In this article, we establish a near-optimal convergence rate for the CLT of linear eigenvalue statistics of Wigner matrices, in Kolmogorov-Smirnov distance. For all test functions…

math.PR2020

Central limit theorem for mesoscopic eigenvalue statistics of the free sum of matrices

Zhigang Bao, Kevin Schnelli, Yuanyuan Xu

We consider random matrices of the form $H_{N} = A_{N} + U_{N} B_{N} U_{N}^{*}$ , where $A_{N}$ , $B_{N}$ are two $N$ by $N$ deterministic Hermitian matrices and $U_{N}$ is a Haar distributed random unita…

math.PR2019

On Cramér-von Mises statistic for the spectral distribution of random matrices

Zhigang Bao, Yukun He

Let $F_{N}$ and $F$ be the empirical and limiting spectral distributions of an $N \times N$ Wigner matrix. The Cramér-von Mises (CvM) statistic is a classical goodness-of-fit statisti…

math.PR2016

Convergence Rate for Spectral Distribution of Addition of Random Matrices

Zhigang Bao, Laszlo Erdos, Kevin Schnelli

Let $A$ and $B$ be two $N$ by $N$ deterministic Hermitian matrices and let $U$ be an $N$ by $N$ Haar distributed unitary matrix. It is well known that the spectral distribution of…

math.PR2015★ 6 cited

Delocalization for a class of random block band matrices

Zhigang Bao, Laszlo Erdos

We consider $N \times N$ Hermitian random matrices $H$ consisting of blocks of size $M \geq N^{6/7}$ . The matrix elements are i.i.d. within the blocks, close to a Gaussian in the fou…

math.PR2011

Local Semicircle law and Gaussian fluctuation for Hermite $β$ ensemble

Zhigang Bao, Zhonggen Su

Let $β > 0$ and consider an $n$ -point process $λ_{1}, λ_{2}, ..., λ_{n}$ from Hermite $β$ ensemble on the real line $R$ . Dumitriu and Edelman discovered a tri-diagonal matrix model…