Published 2021
| Version v1
Journal article
Wick polynomials in noncommutative probability: a group-theoretical approach
- Others:
- Laboratoire Jean Alexandre Dieudonné (JAD) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
- Weierstraß-Institut für Angewandte Analysis und Stochastik = Weierstrass Institute for Applied Analysis and Stochastics [Berlin] (WIAS) ; Forschungsverbund Berlin e.V. (FVB) (FVB)
- Institut für Mathematik [Berlin] ; Technische Universität Berlin (TU)
- Laboratoire de Probabilités, Statistique et Modélisation (LPSM (UMR_8001)) ; Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)
Description
Wick polynomials and Wick products are studied in the context of non-commutative probability theory. It is shown that free, boolean and conditionally free Wick polynomials can be defined and related through the action of the group of characters over a particular Hopf algebra. These results generalize our previous developments of a Hopf algebraic approach to cumulants and Wick products in classical probability theory.
Abstract
International audience
Additional details
- URL
- https://hal.archives-ouvertes.fr/hal-02438241
- URN
- urn:oai:HAL:hal-02438241v1
- Origin repository
- UNICA