Free extreme values

Details Free extreme values Free extreme values

2005-01-18

arxiv.org/abs/math/0501274v2

Annals of Probability 2006, Vol. 34, No. 5, 2037-2059

Mathematics

Operator Algebras

Published at http://dx.doi.org/10.1214/009117906000000016 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117906000000016

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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