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math.PR2024
Matrix Chaos Inequalities and Chaos of Combinatorial Type
Afonso S. Bandeira, Kevin Lucca, Petar Nizić-Nikolac +1
Matrix concentration inequalities and their recently discovered sharp counterparts provide powerful tools to bound the spectrum of random matrices whose entries are linear function…
math.PR2024
A Geometric Perspective on the Injective Norm of Sums of Random Tensors
Afonso S. Bandeira, Sivakanth Gopi, Haotian Jiang +2
Matrix concentration inequalities, intimately connected to the Non-Commutative Khintchine inequality, have been an important tool in both applied and pure mathematics. We study ten…
math.PR2024
Matrix Concentration Inequalities and Free Probability II. Two-sided Bounds and Applications
Afonso S. Bandeira, Giorgio Cipolloni, Dominik Schröder +1
The first paper in this series introduced a new family of nonasymptotic matrix concentration inequalities that sharply capture the spectral properties of very general random matric…