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

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Date of Publication:2021-05-04

Journal:COMMUNICATIONS IN STATISTICS-THEORY AND METHODS

Volume:50

Issue:10

Page Number:2419-2428

ISSN No.:0361-0926

Key Words:random matrix; folded Gaussian distribution; tail bound; the largest singular value; expectation bound

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.