Shifted Substitution in Non-Commutative Multivariate Power Series with a View Toward Free Probability

Nikolas Tapia (WIAS, Berlin)

Feb 20. 2025, 12:00 — 12:30

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.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Files:
Slides
Associated Event:
Recent Perspectives on Non-crossing Partitions through Algebra, Combinatorics, and Probability (Workshop)
Organizer(s):
Adrian Celestino Rodriguez (TU Graz)
Kurusch Ebrahimi-Fard (NTNU, Trondheim)
James Mingo (Queen's U, Kingston)
Martin Rubey (TU Vienna)
Eleni Tzanaki (U of Crete)
Yannic Vargas (CUNEF U, Madrid)