arXiv math/05012742005-01math.OAmath.PR

Free extreme values

Gerard Ben Arous, Dan Virgil Voiculescu

备注：: Published at http://dx.doi.org/10.1214/009117906000000016 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
发表信息：: Annals of Probability 2006, Vol. 34, No. 5, 2037-2059
DOI：: 10.1214/009117906000000016

英文摘要：

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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