2013/05/03 by Daniel Paulin, Lester Mackey, Paulin, Daniel +3 · 7 citations
Mathematics · #60B20 #60E15 #60F10 #60G09 #Bernstein inequalities #Bounded function #Combinatorics #Concentration inequality #Discrete mathematics #Eigenvalues and eigenvectors #Extension (predicate logic) #FOS: Mathematics #Functional Analysis (math.FA) #G.3 #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematical proof #Mathematics #Matrix (chemical analysis) #Point processes and geometric inequalities #Probability (math.PR) #Pure mathematics #Random Matrices and Applications #Random matrix #Random variable #Singular value #Statistics #acm:60B20 #acm:60E15 #acm:60F10 #acm:60G09 #math.FA #math.PR #msc:60B20 #msc:60E15 #msc:60F10 #msc:60G09
paper · pdf · doi:10.48550/arxiv.1305.0612
published in arXiv (Cornell University) (Cornell University) · 29 pages
arxiv created 2013/05/03 · openalex publication_date 2013/05/03 · arxiv updated 2013/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
This paper derives exponential tail bounds and polynomial moment inequalities for the spectral norm deviation of a random matrix from its mean value. The argument depends on a matrix extension of Stein's method of exchangeable pairs for concentration of measure, as introduced by Chatterjee. Recent work of Mackey et al. uses these techniques to analyze random matrices with additive structure, while the enhancements in this paper cover a wider class of matrix-valued random elements. In particular, these ideas lead to a bounded differences inequality that applies to random matrices constructed from weakly dependent random variables. The proofs require novel trace inequalities that may be of independent interest.