Central limit theorem; Dyson’s brownian motion; Matrix-valued ornstein-uhlenbeck process; Particle system; Squared bessel particle system; Wishart process; Statistics and Probability; Statistics, Probability and Uncertainty
Abstract :
[en] 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 matrixvalued Ornstein-Uhlenbeck process is obtained.
Disciplines :
Mathematics
Author, co-author :
Song, Jian; Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao, China ; School of Mathematics, Shandong University, Jinan, China
Yao, Jianfeng; Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong
YUAN, Wangjun ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) ; Department of Mathematics, The University of Hong Kong, Hong Kong
External co-authors :
yes
Language :
English
Title :
High-dimensional central limit theorems for a class of particle systems*
Publication date :
2021
Journal title :
Electronic Journal of Probability
eISSN :
1083-6489
Publisher :
Institute of Mathematical Statistics
Volume :
26
Issue :
none
Peer reviewed :
Peer Reviewed verified by ORBi
Funding text :
*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. †Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao, Shan-dong, 266237, China and School of Mathematics, Shandong University, Jinan, Shandong, 250100, China.
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