Shuffle algebras in operator-valued probability theory.

Nicolas Gilliers (NTNU, Trondheim)

Oct 16. 2020, 13:15 — 14:00

In this talk I will explain the basics of operator-valued free non-commutative probability theory. Then, using operads and 2-monoidal categories, we will extend the shuffle algebras approach to free, boolean and monotone moment-cumulant relations (see Ebrahimi-Fard & Patras, shuffle group laws : applications in free probability) to their operator-valued counterparts. I will end this talk with loose ends related to free multiplicative operator-valued convolution and potential use of shuffle algebras in this context.

arXiv:2005.12049, Gilliers Nicolas, A shuffle algebra point of view on operator-valued probability theory


Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Higher Structures Emerging from Renormalisation - partially postponed (Online Workshop)
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)