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2021 High-dimensional central limit theorems for a class of particle systems
Jian Song, Jianfeng Yao, Wangjun Yuan
Author Affiliations +
Electron. J. Probab. 26: 1-33 (2021). DOI: 10.1214/21-EJP646


We consider a class of particle systems that generalizes the eigenvalues of a class of matrix-valued processes, of which the empirical measures converge to deterministic measures as the dimension goes to infinity. In this paper, we obtain central limit theorems (CLTs) to characterize the fluctuations of the empirical measures around the limit measures by using stochastic calculus. As applications, CLTs for Dyson’s Brownian motion and the eigenvalues of Wishart process are recovered under slightly more general initial conditions, and a CLT for the eigenvalues of a symmetric matrix-valued Ornstein-Uhlenbeck process is obtained.

Funding Statement

J. Song is supported by Shandong University grant 11140089963041 and National Natural Science Foundation of China grant 12071256. J. Yao is supported by HKSAR-RGC-Grant GRF-17307319.


The authors are grateful to the referees for their valuable and detailed comments.


Download Citation

Jian Song. Jianfeng Yao. Wangjun Yuan. "High-dimensional central limit theorems for a class of particle systems." Electron. J. Probab. 26 1 - 33, 2021.


Received: 25 March 2020; Accepted: 22 May 2021; Published: 2021
First available in Project Euclid: 22 June 2021

Digital Object Identifier: 10.1214/21-EJP646

Primary: 60F05, 60H15


Vol.26 • 2021
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