${\epsilon}$-Noncrossing Partitions and Cumulants in Free Probability. (22nd May 2017)

• Record Type: Journal Article
• Authors: Ebrahimi-Fard, Kurusch; Patras, Frédéric; Speicher, Roland
• Is Part Of: International mathematics research notices. Volume 2018:Number 23(2018)
• Page Start: 7156
• Page End: 7170
• Publication Date: 2017-05-22
• Subjects: 46L54 -- 06A07; Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnx098
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: Motivated by recent work on mixtures of classical and free probabilities, we introduce and study the notion of $\epsilon$ -noncrossing partitions. It is shown that the set of such partitions forms a lattice. It is a subposet of the poset of partitions and it contains the one of noncrossing partitions. Moreover, $\epsilon$ -cumulants are introduced and shown to characterize the notion of $\epsilon$ -independence.