Subadditivity of Matrix phi-Entropy and Concentration of Random Matrices

Abstract

Matrix concentration inequalities provide a direct way to bound the typical spectral norm of a random matrix. The methods for establishing these results often parallel classical arguments, such as the Laplace transform method. This work develops a matrix extension of the entropy method, and it applies these ideas to obtain some matrix concentration inequalities.

23 pages

References in corpus (3)

• Moment inequalities for functions of independent random variables
• Characterisation of matrix entropies
• Deriving Matrix Concentration Inequalities from Kernel Couplings

Cited by in corpus (9)

• On the joint convexity of the Bregman divergence of matrices
• Exponential Decay of Matrix $\Phi$-Entropies on Markov Semigroups with Applications to Dynamical Evolutions of Quantum Ensembles
• Matrix Poincaré, Φ-Sobolev inequalities, and quantum ensembles
• Nonlinear Matrix Concentration via Semigroup Methods
• From Poincaré Inequalities to Nonlinear Matrix Concentration
• A Matrix Bernstein Inequality for Strong Rayleigh Distributions
• Jointly convex quantum Jensen divergences
• A note on quantum entropy
• Some operator convex functions of several variables