Dimension-free bounds for largest singular values of matrix Gaussian series

Xianjie Gao, Chao Zhang and Hongwei Zhang

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 10, 2419-2428

Abstract: The matrix Gaussian series refers to a sum of fixed matrices weighted by independent standard normal variables and plays an important in various fields related to probability theory. In this paper, we present the dimension-free tail bounds and expectation bounds for the largest singular value (LSV) of matrix Gaussian series, respectively. By using the resulting bounds, we compute the expectation bounds for LSVs of Gaussian Wigner matrix and Gaussian Toeplitz matrix, respectively.

Date: 2021
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DOI: 10.1080/03610926.2019.1670846

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