Free extreme values
Operator Algebras
2007-05-23 v2 Probability
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.
Cite
@article{arxiv.math/0501274,
title = {Free extreme values},
author = {Gerard Ben Arous and Dan Virgil Voiculescu},
journal= {arXiv preprint arXiv:math/0501274},
year = {2007}
}
Comments
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)