Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices

Kevin Schnelli, Yuanyuan Xu

Type: Article

Publication Date: 2022-04-15

Citations: 6

DOI: https://doi.org/10.1007/s00220-022-04377-y

View Publication

Download PDF

Abstract

We show that the fluctuations of the largest eigenvalue of a real symmetric or complex Hermitian Wigner matrix of size

Locations

Communications in Mathematical Physics - View - PDF
PubMed Central - View
arXiv (Cornell University) - View - PDF
PubMed - View
DataCite API - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices	2023	Kevin Schnelli Yuanyuan Xu
+ PDF Chat	Quantitative Tracy–Widom laws for the largest eigenvalue of generalized Wigner matrices	2023	Kevin Schnelli Yuanyuan Xu
+ PDF Chat	Quantitative universality for the largest eigenvalue of sample covariance matrices	2024	Haoyu Wang
+	Quantitative Tracy-Widom laws for the largest eigenvalue of generalized Wigner matrices	2022	Kevin Schnelli Yuanyuan Xu
+	Functional Central Limit Theorems for Wigner Matrices	2020	Giorgio Cipolloni László Erdős Dominik Schröder
+	Fluctuations in the spectrum of non-Hermitian i.i.d. matrices	2022	Giorgio Cipolloni
+ PDF Chat	CONVERGENCE RATE OF EXPECTED SPECTRAL DISTRIBUTIONS OF LARGE RANDOM MATRICES PART I: WIGNER MATRICES	2008	Zhidong Bai
+ PDF Chat	Functional central limit theorems for Wigner matrices	2023	Giorgio Cipolloni László Erdős Dominik Schröder
+ PDF Chat	Tracy-Widom limit for the largest eigenvalue of high-dimensional covariance matrices in elliptical distributions	2022	Wen Jun Xie Jiahui Long Yu Zhou Wang
+ PDF Chat	Central limit theorem for mesoscopic eigenvalue statistics of deformed Wigner matrices and sample covariance matrices	2021	Yiting Li Kevin Schnelli Yuanyuan Xu
+	Tracy-Widom limit for the largest eigenvalue of high-dimensional covariance matrices in elliptical distributions	2019	Jun Wen Zhou Wang
+ PDF Chat	Small deviation estimates for the largest eigenvalue of Wigner matrices	2023	László Erdős Yuanyuan Xu
+	Small deviation estimates for the largest eigenvalue of Wigner matrices	2021	László Erdős Yuanyuan Xu
+	Extreme gaps between eigenvalues of Wigner matrices	2021	Paul Bourgade
+ PDF Chat	A rate of convergence result for the largest eigenvalue of complex white Wishart matrices	2006	Noureddine El Karoui
+	Accuracy of the Tracy-Widom limit for the largest eigenvalue in white Wishart matrices	2008	Zongming Ma
+ PDF Chat	A necessary and sufficient condition for edge universality at the largest singular values of covariance matrices	2018	Xiucai Ding Fan Yang
+	Accuracy of the Tracy–Widom limits for the extreme eigenvalues in white Wishart matrices	2012	Zongming Ma
+ PDF Chat	Eigenvalues for the minors of Wigner matrices	2022	Jiaoyang Huang
+ PDF Chat	Quantitative CLT for linear eigenvalue statistics of Wigner matrices	2023	Zhigang Bao Yukun He

Works That Cite This (6)

Action	Title	Year	Authors
+ PDF Chat	Precise asymptotics for the spectral radius of a large random matrix	2024	Giorgio Cipolloni László Erdős Yuanyuan Xu
+ PDF Chat	Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices	2022	Kevin Schnelli Yuanyuan Xu
+ PDF Chat	Phase transition for the smallest eigenvalue of covariance matrices	2024	Zhigang Bao Jaehun Lee Xiaocong Xu
+ PDF Chat	Quantitative Tracy–Widom laws for the largest eigenvalue of generalized Wigner matrices	2023	Kevin Schnelli Yuanyuan Xu
+ PDF Chat	Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices	2023	Kevin Schnelli Yuanyuan Xu
+	On the rightmost eigenvalue of non-Hermitian random matrices	2023	Giorgio Cipolloni László Erdős Dominik Schröder Yuanyuan Xu

Works Cited by This (45)

Action	Title	Year	Authors
+	Random matrices and determinantal processes	2005	Kurt Johansson
+	None	2003	C. Benoît
+ PDF Chat	A rate of convergence result for the largest eigenvalue of complex white Wishart matrices	2006	Noureddine El Karoui
+ PDF Chat	Fast approach to the Tracy–Widom law at the edge of GOE and GUE	2012	Iain M. Johnstone Zongming Ma
+	Estimates of the Hermite and the Freud polynomials	1990	Stanford S. Bonan Dean S. Clark
+ PDF Chat	Rigidity of eigenvalues of generalized Wigner matrices	2011	László Erdős Horng‐Tzer Yau Jun Yin
+ PDF Chat	Wigner Random Matrices with Non-Symmetrically Distributed Entries	2007	Sandrine Péché Alexander Soshnikov
+ PDF Chat	Central limit theorem for linear eigenvalue statistics of random matrices with independent entries	2009	Anna Lytova L. А. Pastur
+	Asymptotic distribution of smoothed eigenvalue density. II. Wigner random matrices	1999	Anne Boutet de Monvel A. Khorunzhy
+ PDF Chat	Integration with Respect to the Haar Measure on Unitary, Orthogonal and Symplectic Group	2006	C. Benoît Piotr Śniady