Open Access
September 2006 Free extreme values
Gerard Ben Arous, Dan Virgil Voiculescu
Ann. Probab. 34(5): 2037-2059 (September 2006). DOI: 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.


Download Citation

Gerard Ben Arous. Dan Virgil Voiculescu. "Free extreme values." Ann. Probab. 34 (5) 2037 - 2059, September 2006.


Published: September 2006
First available in Project Euclid: 14 November 2006

zbMATH: 1117.46044
MathSciNet: MR2271490
Digital Object Identifier: 10.1214/009117906000000016

Primary: 46L53 , 46L54 , 60G70

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

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 5 • September 2006
Back to Top