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Small-Deviation Inequalities for Sums of Random Matrices
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 of 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 the high-dimensional and even the
infinite-dimensional cases
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