Algebraic structures for cumulants in non-commutative probability theory
- Kurusch Ebrahimi-Fard (Norwegian University of Science and Technology, Trondheim)
In this talk, we will discuss several algebraic structures relevant to the concise description of relations between the R- and S-transforms in non-commutative probability theory. This includes shuffle, pre- and post-Lie algebras. We will focus on Dykema’s so-called twisted factorisation formula for Voiculescu's S-transform, which can be understood in an operadic framework.
Based on joint work F. Patras (CNRS, Nice, FR) and N. Gilliers (IMT, Toulouse, FR).