Yannic Vargas (University of Potsdam)
The study of relations between moments and cumulants plays a central role in both classical and non-commutative probability theory. In the last decade, the work of Patras and Ebrahimi-Fard provided several tools related to the group of characters on a combinatorial Hopf algebra H of "words on words", and its corresponding Lie algebra of infinitesimal characters. This enables the study of distinct families of cumulants corresponding to different types of independences: free, boolean and monotone. We discuss several formulas for the (known) free-to-moment and boolean-to-moment relations, obtained from the antipode of H. Also, using a weighted Möbius inversion, we deduce a new relation of monotone cumulants in terms of moments.
For those of you who can and would like to join us, please meet us in the seminar Room 2.22 of the maths institute, where we can follow the talk together.
You are welcome to invite your friends and colleagues to join us! If you wish to attend the talks, please contact Sylvie Paycha firstname.lastname@example.org for the login details.