Almost sure convergence of the largest and smallest eigenvalues of high-dimensional sample correlation matrices

DOI10.1016/j.spa.2017.10.002zbMath1388.60027arXiv2001.11459OpenAlexW2766778349MaRDI QIDQ1639676

Johannes Heiny, Thomas Mikosch

Publication date: 13 June 2018

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.11459

zbMATH Keywords

combinatoricsregular variationlargest eigenvaluesmallest eigenvaluespectral distributionsample covariance matrixsample correlation matrixself-normalizationinfinite fourth moment

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Random matrices (probabilistic aspects) (60B20) Stationary stochastic processes (60G10) Extreme value theory; extremal stochastic processes (60G70) Large deviations (60F10) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (9)

The volume of random simplices from elliptical distributions in high dimension ⋮ Logarithmic law of large random correlation matrices ⋮ Large sample autocovariance matrices of linear processes with heavy tails ⋮ High-dimensional sample covariance matrices with Curie-Weiss entries ⋮ Random matrix theory for heavy-tailed time series ⋮ Thin-shell theory for rotationally invariant random simplices ⋮ Large sample correlation matrices: a comparison theorem and its applications ⋮ The asymptotic distribution of the condition number for random circulant matrices ⋮ Limiting distributions for eigenvalues of sample correlation matrices from heavy-tailed populations

Uses Software

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