Kevin Schnelli

activity

20132026

most citedEdge Universality for Deformed Wigner Matrices

78 citations · 199 across the 22 of their papers we have counts for

collaborators

26 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.PR2025

Quantitative Tracy-Widom laws for sparse random matrices

Teodor Bucht, Kevin Schnelli, Yuanyuan Xu

We consider the fluctuations of the largest eigenvalue of sparse random matrices, the class of random matrices that includes the normalized adjacency matrices of the Erdős-Rényi gr…

math.PR2023

The free energy of matrix models

Félix Parraud, Kevin Schnelli

In this paper we study multi-matrix models whose potentials are perturbations of the quadratic potential associated with independent GUE random matrices. More precisely, we compute…

math.PR2022

Quantitative Tracy-Widom laws for the largest eigenvalue of generalized Wigner matrices

Kevin Schnelli, Yuanyuan Xu

We show that the fluctuations of the largest eigenvalue of any generalized Wigner matrix $H$ converge to the Tracy-Widom laws at a rate nearly $O (N^{- 1/3})$ , as the matrix dimensio…

math.PR2022

Asymptotic freeness through unitaries generated by polynomials of Wigner matrices

Félix Parraud, Kevin Schnelli

We study products of functions evaluated at self-adjoint polynomials in deterministic matrices and independent Wigner matrices; we compute the deterministic approximations of such…

math.PR2022★ 1 cited

The support of the free additive convolution of multi-cut measures

Philippe Moreillon, Kevin Schnelli

We consider the free additive convolution $μ_{α} ⊞ μ_{β}$ of two probability measures $μ_{α}$ and $μ_{β}$ , supported on respectively $n_{α}$ and $n_{β}$ disjoint bounded intervals on the…

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.PR2021★ 9 cited

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

Kevin Schnelli, Yuanyuan Xu

We show that the fluctuations of the largest eigenvalue of a real symmetric or complex Hermitian Wigner matrix of size $N$ converge to the Tracy--Widom laws at a rate $O(N^{-1/3+ω}…

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★ 8 cited

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★ 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.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.PR2016

Local law and Tracy-Widom limit for sparse random matrices

Ji Oon Lee, Kevin Schnelli

We consider spectral properties and the edge universality of sparse random matrices, the class of random matrices that includes the adjacency matrices of the Erdos-Renyi graph mode…

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

Universality for Random Matrix Flows with Time-dependent Density

Laszlo Erdos, Kevin Schnelli

We show that the Dyson Brownian Motion exhibits local universality after a very short time assuming that local rigidity and level repulsion hold. These conditions are verified, hen…

math.PR2014

Tracy-Widom Distribution for the Largest Eigenvalue of Real Sample Covariance Matrices with General Population

Ji Oon Lee, Kevin Schnelli

We consider sample covariance matrices of the form $Q = (Σ^{1/2} X) (Σ^{1/2} X)^{*}$ , where the sample $X$ is an $M \times N$ random matrix whose entries are real independent ra…

math.PR2014★ 78 cited

Edge Universality for Deformed Wigner Matrices

Ji Oon Lee, Kevin Schnelli

We consider $N \times N$ random matrices of the form $H = W + V$ where $W$ is a real symmetric Wigner matrix and $V$ a random or deterministic, real, diagonal matrix whose entries a…

math.PR2014★ 72 cited

Bulk universality for deformed Wigner matrices

Ji Oon Lee, Kevin Schnelli, Ben Stetler +1

We consider $N \times N$ random matrices of the form $H = W + V$ where $W$ is a real symmetric or complex Hermitian Wigner matrix and $V$ is a random or deterministic, real, diagonal ma…

math.PR2013★ 1 cited

Extremal Eigenvalues and Eigenvectors of Deformed Wigner Matrices

Ji Oon Lee, Kevin Schnelli

We consider random matrices of the form $H = W + λV$ , $λ \in R^{+}$ , where $W$ is a real symmetric or complex Hermitian Wigner matrix of size $N$ and $V$ is a real bounded dia…

math-ph2013★ 2 cited

Quantum Diffusion with Drift and the Einstein Relation II

Wojciech De Roeck, Juerg Froehlich, Kevin Schnelli

This paper is a companion to 'Quantum Diffusion with Drift and the Einstein Relation I' (jointly submitted to arXiv). Its purpose is to describe and prove a certain number of techn…