Matrix Concentration for Products

Abstract

This paper develops nonasymptotic growth and concentration bounds for a product of independent random matrices. These results sharpen and generalize recent work of Henriksen-Ward, and they are similar in spirit to the results of Ahlswede-Winter and of Tropp for a sum of independent random matrices. The argument relies on the uniform smoothness properties of the Schatten trace classes.

arXiv comment21 pages

References in corpus (4)

• Concentration of the adjacency matrix and of the Laplacian in random graphs with independent edges
• Lecture Notes on "Free Probability Theory"
• Schwinger-Dyson and loop equations for a product of square Ginibre random matrices
• Products of Complex Rectangular and Hermitian Random Matrices

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• Nonlinear Matrix Concentration via Semigroup Methods
• Streaming k-PCA: Efficient guarantees for Oja's algorithm, beyond rank-one updates
• A matrix concentration inequality for products