Free extreme values

DOI10.1214/009117906000000016zbMath1117.46044arXivmath/0501274OpenAlexW3098191884MaRDI QIDQ858990

Gérard Ben Arous, Dan-Virgil Voiculescu

Publication date: 12 January 2007

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0501274

zbMATH Keywords

extreme-value theoryfree probabilityfree extremal convolutionsfree Poisson point process

Mathematics Subject Classification ID

Extreme value theory; extremal stochastic processes (60G70) Free probability and free operator algebras (46L54) Noncommutative probability and statistics (46L53)

Related Items (15)

Free point processes and free extreme values ⋮ Some properties of the free stable distributions ⋮ The maximum domain of attraction of multivariate extreme value distributions is small ⋮ Free subexponentiality ⋮ The Bi-free Extension of Free Probability ⋮ Max-convolution semigroups and extreme values in limit theorems for the free multiplicative convolution ⋮ Free probability for pairs of faces. IV: Bi-free extremes in the plane ⋮ Semicircular limits on the free Poisson chaos: counterexamples to a transfer principle ⋮ A matrix interpolation between classical and free max operations. I: The univariate case ⋮ Boolean convolutions and regular variation ⋮ Bi-free extreme values ⋮ Homomorphisms relative to additive convolutions and max-convolutions: Free, boolean and classical cases ⋮ Applying free random variables to random matrix analysis of financial data. Part I: The Gaussian case ⋮ Boolean extremes and Dagum distributions ⋮ Limit theorems for classical, freely and Boolean max-infinitely divisible distributions

Cites Work

• Estimating tails of probability distributions
• Majorization, doubly stochastic matrices, and comparison of eigenvalues
• Lévy-Hinčin type theorems for multiplicative and additive free convolution
• Residual life time at great age
• Statistical inference using extreme order statistics
• Stable laws and domains of attraction in free probability theory
• Free Random Variables
• On the multiplication of free N -tuples of noncommutative random variables
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