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Free Extreme Values

Gerard Ben Arous and Dan Virgil Voiculescu
The Annals of Probability
Vol. 34, No. 5 (Sep., 2006), pp. 2037-2059
Stable URL: http://www.jstor.org/stable/25449943
Page Count: 23
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Free Extreme Values
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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.

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