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Article

Optimized Tail Bounds for Random Matrix Series

by
Xianjie Gao
1,*,
Mingliang Zhang
2 and
Jinming Luo
3
1
Department of Basic Sciences, Shanxi Agricultural University, Jinzhong 030801, China
2
School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
3
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
*
Author to whom correspondence should be addressed.
Entropy 2024, 26(8), 633; https://doi.org/10.3390/e26080633
Submission received: 24 June 2024 / Revised: 22 July 2024 / Accepted: 26 July 2024 / Published: 26 July 2024
(This article belongs to the Special Issue Random Matrix Theory and Its Innovative Applications)

Abstract

Random matrix series are a significant component of random matrix theory, offering rich theoretical content and broad application prospects. In this paper, we propose modified versions of tail bounds for random matrix series, including matrix Gaussian (or Rademacher) and sub-Gaussian and infinitely divisible (i.d.) series. Unlike present studies, our results depend on the intrinsic dimension instead of ambient dimension. In some cases, the intrinsic dimension is much smaller than ambient dimension, which makes the modified versions suitable for high-dimensional or infinite-dimensional setting possible. In addition, we obtain the expectation bounds for random matrix series based on the intrinsic dimension.
Keywords: tail bound; intrinsic dimension; random matrix series; expectation bound tail bound; intrinsic dimension; random matrix series; expectation bound

Share and Cite

MDPI and ACS Style

Gao, X.; Zhang, M.; Luo, J. Optimized Tail Bounds for Random Matrix Series. Entropy 2024, 26, 633. https://doi.org/10.3390/e26080633

AMA Style

Gao X, Zhang M, Luo J. Optimized Tail Bounds for Random Matrix Series. Entropy. 2024; 26(8):633. https://doi.org/10.3390/e26080633

Chicago/Turabian Style

Gao, Xianjie, Mingliang Zhang, and Jinming Luo. 2024. "Optimized Tail Bounds for Random Matrix Series" Entropy 26, no. 8: 633. https://doi.org/10.3390/e26080633

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