The Annals of Probability

Free extreme values

Gerard Ben Arous and Dan Virgil Voiculescu

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Abstract

Free probability analogs of the basics of extreme-value theory are obtained, based on Ando’s spectral order. This includes classification of freely max-stable laws and their domains of attraction, using “free extremal convolutions” on the distributions. These laws coincide with the limit laws in the classical peaks-over-threshold approach. A free extremal projection-valued process over a measure-space is constructed, which is related to the free Poisson point process.

Article information

Source
Ann. Probab., Volume 34, Number 5 (2006), 2037-2059.

Dates
First available in Project Euclid: 14 November 2006

Permanent link to this document
https://projecteuclid.org/euclid.aop/1163517232

Digital Object Identifier
doi:10.1214/009117906000000016

Mathematical Reviews number (MathSciNet)
MR2271490

Zentralblatt MATH identifier
1117.46044

Subjects
Primary: 46L54: Free probability and free operator algebras 60G70: Extreme value theory; extremal processes 46L53: Noncommutative probability and statistics

Keywords
Free max-stable laws free extremal process generalized Pareto laws Ando spectral order

Citation

Arous, Gerard Ben; Voiculescu, Dan Virgil. Free extreme values. Ann. Probab. 34 (2006), no. 5, 2037--2059. doi:10.1214/009117906000000016. https://projecteuclid.org/euclid.aop/1163517232


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