Published October 7, 2022
| Version v1
Publication
Shifted substitution in non-commutative multivariate power series with a view toward free probability
- Others:
- Norwegian University of Science and Technology [Aalesund] (NTNU) ; Norwegian University of Science and Technology (NTNU)
- Université Côte d'Azur (UCA)
- Weierstraß-Institut für Angewandte Analysis und Stochastik = Weierstrass Institute for Applied Analysis and Stochastics [Berlin] (WIAS) ; Forschungsverbund Berlin e.V. (FVB) (FVB)
- Technische Universität Berlin (TU)
- Sorbonne Université (SU)
Description
We study a particular group law on formal power series in non-commuting variables induced by their interpretation as linear forms on a suitable graded connected word Hopf algebra. This group law is left-linear and is therefore associated to a pre-Lie structure on formal power series. We study these structures and show how they can be used to recast in a group theoretic form various identities and transformations on formal power series that have been central in the context of non-commutative probability theory, in particular in Voiculescu's theory of free probability.
Additional details
- URL
- https://hal.archives-ouvertes.fr/hal-03806591
- URN
- urn:oai:HAL:hal-03806591v1
- Origin repository
- UNICA