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Free extreme values. (English) Zbl 1117.46044

Summary: 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.

MSC:

46L54 Free probability and free operator algebras
60G70 Extreme value theory; extremal stochastic processes
46L53 Noncommutative probability and statistics
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