New formulas for cumulant-to-moment relations

Yannic Vargas (TU Graz)

Nov 11. 2021, 16:00 — 16:25

The study of relations between moments and cumulants play a central role in both classical and non-commutative probability theory. In the last decade, the work of Patras and Ebrahimi-Fard has provided several tools to use the group of characters on a combinatorial Hopf algebra H of "words on words", and its corresponding Lie algebra of infinitesimal characters, to study 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.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Higher Structures Emerging from Renormalisation (Graduate School)
Pierre Clavier (U of Haut-Alsace)
Kurusch Ebrahimi-Fard (NTNU, Trondheim)
Peter K. Friz (TU Berlin)
Harald Grosse (U of Vienna)
Dominique Manchon (U Clerment Auvergne)
Sylvie Paycha (U of Potsdam)
Sylke Pfeiffer (U of Potsdam)