User-Friendly Tail Bounds for Sums of Random Matrices

• Published in: Foundations of computational mathematics Vol. 12; no. 4; pp. 389 - 434
• Main Author: Tropp, Joel A.
• Format: Journal Article
• Language: English
• Published: New York Springer-Verlag 01.08.2012; Springer; Springer Nature B.V
• Subjects: Algorithms; Applications of Mathematics; Computer Science; Economics; Eigenvalues; Linear and Multilinear Algebras; Math Applications in Computer Science; Mathematics; Mathematics and Statistics; Matrix Theory; Numerical Analysis; Probability; Random matrix; 60F10; 60G42; Discrete-time martingale; Sum of independent random variables; 60G50; Probability inequality; 60B20; Large deviation

This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the large-deviation behavior of the maximum eigenvalue of the sum. Tail boun...