Title of Paper:Small-Deviation Inequalities for Sums of Random Matrices

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Date of Publication:2019-05-01

Journal:SYMMETRY-BASEL

Included Journals:SCIE

Volume:11

Issue:5

ISSN No.:2073-8994

Key Words:large-deviation inequality; small-deviation inequality; random matrix; largest singular value

Abstract:Random matrices have played an important role in many fields including machine learning, quantum information theory, and optimization. One of the main research focuses is on the deviation inequalities for eigenvalues of random matrices. Although there are intensive studies on the large-deviation inequalities for random matrices, only a few works discuss the small-deviation behavior of random matrices. In this paper, we present the small-deviation inequalities for the largest eigenvalues of sums of random matrices. Since the resulting inequalities are independent of the matrix dimension, they are applicable to high-dimensional and even the infinite-dimensional cases.