Malte Gerhold (Université de la Sarre) : Classification of two-faced independences
Abstract: Two-faced independences are independence relations for pairs of noncommutative random variables. An important example is bifree
independence, which models the relation between left and right regular representation of the free group in the canonical tracial state. Around
2000, in works of Speicher, Ben Ghorbal & Schürmann, and Muraki, a complete classification of « single-faced » independences was obtained:
the only independences in this case are boolean, tensor, free, monotone and anti-monotone independence. I report on the current status of the
classification program for two (or multi-faced) independences and we will focus on the interplay between the lifting approach (discussed in
the preceding talk, given by Takahiro Hasebe) and the combinatorial « cumulant » approach to multi-faced independences.
Based on joint work with Takahiro Hasebe, Michaël Ulrich, and Philipp Varšo.