Deviation inequalities for the spectral norm of structured random matrices

Guozheng Dai and Zhonggen Su

Statistics & Probability Letters, 2025, vol. 221, issue C

Abstract: We study the deviation inequality for the spectral norm of structured random matrices with non-gaussian entries. In particular, we establish an optimal bound for the p-th moment of the spectral norm by transfering the spectral norm into the suprema of canonical processes. A crucial ingredient of our proof is a comparison of weak and strong moments. As an application, we show a deviation inequality for the smallest singular value of a rectangular random matrix.

Keywords: Comparison of weak and strong moments; Contraction principle; Deviation inequality; Spectral norm (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2025.110378

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