Asymptotic Freeness for Rectangular Random Matrices and Large Deviations\n for Sample Covariance Matrices With Sub-Gaussian Tails

2015/05/21 by Benjamin Groux, Groux, Benjamin · 5 citations
Mathematics · #Advanced Algebra and Geometry #Combinatorics #Convolution (computer science) #Covariance #Covariance matrix #Eigenvalues and eigenvectors #FOS: Mathematics #Gaussian #Large deviations theory #Mathematics #Matrix (chemical analysis) #Measure (data warehouse) #Point processes and geometric inequalities #Probability (math.PR) #Pure mathematics #Random Matrices and Applications #Random matrix #Sample mean and sample covariance #Statistics #math.PR

paper · pdf · doi:10.48550/arxiv.1505.05733

published in arXiv (Cornell University) (Cornell University)

arxiv created 2015/05/21 · openalex publication_date 2015/05/21 · arxiv updated 2015/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We establish a large deviation principle for the empirical spectral measure\nof a sample covariance matrix with sub-Gaussian entries, which extends\nBordenave and Caputo's result for Wigner matrices having the same type of\nentries [7]. To this aim, we need to establish an asymptotic freeness result\nfor rectangular free convolution, more precisely, we give a bound in the\nsubordination formula for information-plus-noise matrices.\n

Citations

• On the Distribution of the Roots of Certain Symmetric Matrices

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