Free extreme values

• 成果类型: Article
• 署名作者: Ben Arous, Gerard; Voiculescu, Dan Virgil
• 署名单位: New York University; University of California System; University of California Berkeley
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000016
• 发表日期: 2006
• 页码: 2037-2059
• 关键词: free convolution

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.