${ε}$-Noncrossing Partitions and Cumulants in Free Probability. (22nd May 2017) - 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 $ε$ -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, $ε$ -cumulants are introduced and shown to characterize the notion of $ε$ -independence.