Z. Bao

activity

20112026

most citedUniversality for the largest eigenvalue of sample covariance matrices with general population

101 citations · 243 across the 33 of their papers we have counts for

collaborators

33 papers

math.PR2026

Order statistics for edge eigenvectors of Wigner matrices

Zhigang Bao, Teodor Bucht, Kevin Schnelli

In this paper, we establish a general comparison theorem for the order statistics of the edge eigenvectors for generalized Wigner matrices. Consequently, we derive the Gumbel law f…

math.PR2026

Eigenvector distribution of random matrices under critical finite-rank deformations

Zhigang Bao, Dong Wang, Yue Zhu

We investigate the eigenvector distribution at the soft edge for Gaussian random matrices with finite-rank deformations, in the critical regime of BBP transition. For finite-rank d…

math.ST2026

A spectral approach for online covariance change point detection

Zhigang Bao, Kha Man Cheong, Yuji Li +1

Change point detection in covariance structures is a fundamental and crucial problem for sequential data. Under the high-dimensional setting, most of the existing research has focu…

math.PR2023★ 2 cited

Phase transition for the smallest eigenvalue of covariance matrices

Zhigang Bao, Jaehun Lee, Xiaocong Xu

In this paper, we study the smallest non-zero eigenvalue of the sample covariance matrices $S (Y) = Y Y^{*}$ , where $Y = (y_{ij})$ is an $M \times N$ matrix with iid mean $0$ vari…

math.PR2022

Extreme eigenvalues of Log-concave Ensemble

Zhigang Bao, Xiaocong Xu

In this paper, we consider the log-concave ensemble of random matrices, a class of covariance-type matrices $X X^{*}$ with isotropic log-concave $X$ -columns. A main example is the cov…

math.ST2022★ 3 cited

Spectral Statistics of Sample Block Correlation Matrices

Zhigang Bao, Jiang Hu, Xiaocong Xu +1

A fundamental concept in multivariate statistics, sample correlation matrix, is often used to infer the correlation/dependence structure among random variables, when the population…

stat.ME2021★ 1 cited

Non-splitting Neyman-Pearson Classifiers

Jingming Wang, Lucy Xia, Zhigang Bao +1

The Neyman-Pearson (NP) binary classification paradigm constrains the more severe type of error (e.g., the type I error) under a preferred level while minimizing the other (e.g., t…

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.ST2020

Statistical inference for principal components of spiked covariance matrices

Zhigang Bao, Xiucai Ding, Jingming Wang +1

In this paper, we study the asymptotic behavior of the extreme eigenvalues and eigenvectors of the high dimensional spiked sample covariance matrices, in the supercritical case whe…

math.PR2020

Eigenvector distribution in the critical regime of BBP transition

Zhigang Bao, Dong Wang

In this paper, we study the random matrix model of Gaussian Unitary Ensemble (GUE) with fixed-rank (aka spiked) external source. We will focus on the critical regime of the Baik-Be…

math-ph2020★ 3 cited

Equipartition principle for Wigner matrices

Zhigang Bao, Laszlo Erdos, Kevin Schnelli

We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a…

math.PR2020★ 3 cited

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.ST2019★ 3 cited

Principal components of spiked covariance matrices in the supercritical regime

Zhigang Bao, Xiucai Ding, Jingming Wang +1

In this paper, we study the asymptotic behavior of the extreme eigenvalues and eigenvectors of the spiked covariance matrices, in the supercritical regime. Specifically, we derive…

math.ST2018★ 16 cited

Singular vector and singular subspace distribution for the matrix denoising model

Zhigang Bao, Xiucai Ding, Ke Wang

In this paper, we study the matrix denosing model $Y = S + X$ , where $S$ is a low-rank deterministic signal matrix and $X$ is a random noise matrix, and both are $M \times n$ . In the sc…

math-ph2018★ 7 cited

On the support of the free additive convolution

Zhigang Bao, Laszlo Erdos, Kevin Schnelli

We consider the free additive convolution of two probability measures $μ$ and $ν$ on the real line and show that $μ ⊞ ν$ is supported on a single interval if $μ$ and $ν$ each…

math.ST2017

Tracy-Widom limit for Kendall's tau

Zhigang Bao

In this paper, we study a high-dimensional random matrix model from nonparametric statistics called the Kendall rank correlation matrix, which is a natural multivariate extension o…

math.PR2017★ 7 cited

Spectral rigidity for addition of random matrices at the regular edge

Zhigang Bao, Laszlo Erdos, Kevin Schnelli

We consider the sum of two large Hermitian matrices $A$ and $B$ with a Haar unitary conjugation bringing them into a general relative position. We prove that the eigenvalue density…

math.ST2017★ 7 cited

Canonical correlation coefficients of high-dimensional Gaussian vectors: finite rank case

Zhigang Bao, Jiang Hu, Guangming Pan +1

Consider a Gaussian vector $z = (x^{'}, y^{'})^{'}$ , consisting of two sub-vectors $x$ and $y$ with dimensions $p$ and $q$ respectively, where both…

math.PR2016★ 1 cited

Local single ring theorem on optimal scale

Zhigang Bao, László Erdős, Kevin Schnelli

Let $U$ and $V$ be two independent $N$ by $N$ random matrices that are distributed according to Haar measure on $U (N)$ . Let $Σ$ be a non-negative deterministic $N$ by $N$ matrix. T…

math.PR2016★ 3 cited

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

Local Stability of the Free Additive Convolution

Zhigang Bao, Laszlo Erdos, Kevin Schnelli

We prove that the system of subordination equations, defining the free additive convolution of two probability measures, is stable away from the edges of the support and blow-up si…

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.ST2014

Test of Independence for High-dimensional Random Vectors Based on Block Correlation Matrices

Zhigang Bao, Jiang Hu, Guangming Pan +1

In this paper, we are concerned with the independence test for $k$ high-dimensional sub-vectors of a normal vector, with fixed positive integer $k$ . A natural high-dimensional exte…