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

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19 papers · 1 filter

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.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.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

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.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.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.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.PR2013★ 101 cited

Universality for the largest eigenvalue of sample covariance matrices with general population

Zhigang Bao, Guangming Pan, Wang Zhou

This paper is aimed at deriving the universality of the largest eigenvalue of a class of high-dimensional real or complex sample covariance matrices of the form $\mathcal{W}_N=Σ^{1…

math.PR2012

Universality for a global property of the eigenvectors of Wigner matrices

Zhigang Bao, Guangming Pan, Wang Zhou

Let $M_{n}$ be an $n \times n$ real (resp. complex) Wigner matrix and $U_{n} Λ_{n} U_{n}^{*}$ be its spectral decomposition. Set $(y_{1}, y_{2} ..., y_{n})^{T} = U_{n}^{*} x$ , where $x = (x_{1}, x_{2}, ...,$ $x_{n})^{T}$ i…

math.PR2012★ 13 cited

The logarithmic law of random determinant

Zhigang Bao, Guangming Pan, Wang Zhou

Consider the square random matrix $A_{n} = (a_{ij})_{n, n}$ , where ${a_{ij} := a_{ij}^{(n)}, i, j = 1, \dots, n}$ is a collection of independent real random variables with means zero and var…

math.PR2012★ 20 cited

Central limit theorem for partial linear eigenvalue statistics of Wigner matrices

Zhigang Bao, Guangming Pan, Wang Zhou

In this paper, we study the complex Wigner matrices $M_{n} = \frac{1}{n} W_{n}$ whose eigenvalues are typically in the interval $[- 2, 2]$ . Let $λ_{1} \leq λ_{2} ... \leq λ_{n}$ be the ordered…

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…

math.PR2011

On asymptotic expansion and CLT of linear eigenvalue statistics for sample covariance matrices when $N / M \to 0$

Zhigang Bao

We study the renormalized real sample covariance matrix $H = X^{T} X / M N - M / N$ with $N / M \to 0$ as $N, M \to \infty$ in this paper. And we always assume $M=M(N)…

Order statistics for edge eigenvectors of Wigner matrices

Eigenvector distribution of random matrices under critical finite-rank deformations

Phase transition for the smallest eigenvalue of covariance matrices

Extreme eigenvalues of Log-concave Ensemble

Quantitative CLT for linear eigenvalue statistics of Wigner matrices

Eigenvector distribution in the critical regime of BBP transition

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

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

Spectral rigidity for addition of random matrices at the regular edge

Local single ring theorem on optimal scale

Convergence Rate for Spectral Distribution of Addition of Random Matrices

Local Stability of the Free Additive Convolution

Delocalization for a class of random block band matrices

Universality for the largest eigenvalue of sample covariance matrices with general population

Universality for a global property of the eigenvectors of Wigner matrices

The logarithmic law of random determinant

Central limit theorem for partial linear eigenvalue statistics of Wigner matrices

Local Semicircle law and Gaussian fluctuation for Hermite β ensemble

On asymptotic expansion and CLT of linear eigenvalue statistics for sample covariance matrices when N/M→0

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

On asymptotic expansion and CLT of linear eigenvalue statistics for sample covariance matrices when $N / M \to 0$