Kevin Schnelli

activity

20152021

collaborators

8 papers

math.PR2021

Convergence rate to the Tracy--Widom laws for the largest eigenvalue of sample covariance matrices

Kevin Schnelli, Yuanyuan Xu

We establish a quantitative version of the Tracy--Widom law for the largest eigenvalue of high dimensional sample covariance matrices. To be precise, we show that the fluctuations…

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

Central limit theorem for mesoscopic eigenvalue statistics of deformed Wigner matrices and sample covariance matrices

Yiting Li, Kevin Schnelli, Yuanyuan Xu

We consider $N$ by $N$ deformed Wigner random matrices of the form $X_{N} = H_{N} + A_{N}$ , where $H_{N}$ is a real symmetric or complex Hermitian Wigner matrix and $A_{N}$ is a deterministic re…

math.PR2018

Local law and Tracy-Widom limit for sparse sample covariance matrices

Jong Yun Hwang, Ji Oon Lee, Kevin Schnelli

We consider spectral properties of sparse sample covariance matrices, which includes biadjacency matrices of the bipartite Erdős-Rényi graph model. We prove a local law for the eig…

math-ph2018

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.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…