Concentration of norms and eigenvalues of random matrices

2002/11/18 by Mark W. Meckes · 1 citation
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Spectral Theory in Mathematical Physics #Stochastic processes and statistical mechanics #math-ph #math.FA #math.MP #math.PR #msc:15A18 #msc:15A52 #msc:15A60 #msc:60F10

paper · pdf · doi:10.1016/s0022-1236(03)00198-8

published as J. Funct. Anal. 211 (2004) no. 2, 508-524 · 15 pages; AMS-LaTeX; updated one reference

arxiv created 2002/11/18 · openalex publication_date 2003/09/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove concentration results for ℓ_pⁿ operator norms of rectangular random matrices and eigenvalues of self-adjoint random matrices. The random matrices we consider have bounded entries which are independent, up to a possible self-adjointness constraint. Our results are based on an isoperimetric inequality for product spaces due to Talagrand.

Citations

• On the distribution of the largest eigenvalue in principal components analysis

Cited by

• On r-to-p norms of random matrices with nonnegative entries: Asymptotic normality and ℓ_∞-bounds for the maximizer

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