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- Title
${\epsilon}$-Noncrossing Partitions and Cumulants in Free Probability.
- Authors
Ebrahimi-Fard, Kurusch; Patras, Frédéric; Speicher, Roland
- 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.
- Subjects
PARTITIONS (Mathematics); CUMULANTS; FREE probability theory; NONCOMMUTATIVE function spaces; PERMUTATIONS
- Publication
IMRN: International Mathematics Research Notices, 2018, Vol 2018, Issue 23, p7156
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnx098