Moment Estimates for the Spectral Norm of Random Matrices with Dependent Entries

arXiv2307.03069MaRDI QIDQ6510950

Hanchao Wang, Zhonggen Su, Guozheng Dai

Abstract: This paper studies the deviation inequality for the spectral norm of random matrices with dependent entries. In particular, we consider a random matrix $BA$, where $A$ is a random matrix with independent mean zero subexponential entries, and $B$ is a deterministic matrix. We obtain an exponential inequality for the spectral norm of an $mimesn$ matrix $BA$ using a comparison theorem due to Latala, van Handel and Youssef. Applying this result, we prove an estimate of the smallest singular value of a random subexponential matrix.

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Functional limit theorems; invariance principles (60F17)

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