Small-Deviation Inequalities for Sums of Random Matrices
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论文类型：期刊论文
发表时间：2019-05-01
发表刊物：SYMMETRY-BASEL
收录刊物：SCIE
卷号：11
期号：5
ISSN号：2073-8994
关键字：large-deviation inequality; small-deviation inequality; random matrix; largest singular value
摘要：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.
发表时间：2019-05-01