Universality and Sharp Matrix Concentration Inequalities

• Published in: Geometric and functional analysis Vol. 34; no. 6; pp. 1734 - 1838
• Main Authors: Brailovskaya, Tatiana, van Handel, Ramon
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.12.2024; Springer Nature B.V
• Subjects: Analysis; Covariance matrix; Inequalities; Mathematics; Mathematics and Statistics; Matrix theory; Phase transitions; Principle of universality; 60E15; 15B52; Random matrices; Free probability; Matrix concentration; 60B20; Universality; 46L53; 46L54

We show that, under mild assumptions, the spectrum of a sum of independent random matrices is close to that of the Gaussian random matrix whose entries have the same mean and covariance. This nonasymptotic universality principle yields sharp matrix concentration inequalities for general sums of inde...