Free extreme values

Gerard Ben Arous, Dan Virgil Voiculescu

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)2037-2059
Number of pages23
JournalAnnals of Probability
Issue number5
StatePublished - Sep 2006


  • Ando spectral order
  • Free extremal process
  • Free max-stable laws
  • Generalized Pareto laws

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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