Concentration and moment inequalities for sums of independent heavy-tailed random matrices

• 成果类型: Article; Early Access
• 署名作者: Jirak, Moritz; Minsker, Stanislav; Shen, Yiqiu; Wahl, Martin
• 署名单位: University of Vienna; University of Southern California; University of Southern California; University of Bielefeld
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-025-01412-6
• 发表日期: 2025
• 关键词: singular-values; bounds

摘要

We prove Fuk-Nagaev and Rosenthal-type inequalities for sums of independent random matrices, focusing on the situation when the norms of the matrices possess finite moments of only low orders. Our bounds depend on the intrinsic dimensional characteristics such as the effective rank, as opposed to the dimension of the ambient space. We illustrate the advantages of such results through several applications, including new moment inequalities for sample covariance matrices and their eigenvectors when the underlying distribution is heavy-tailed. Moreover, we demonstrate that our techniques yield sharpened versions of moment inequalities for empirical processes.