Gaussian Generating Functionals on Easy Quantum Groups

Uwe Franz (), Amaury Freslon () and Adam Skalski ()
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Uwe Franz: Université de Franche-Comté
Amaury Freslon: Université Paris-Saclay, CNRS
Adam Skalski: Institute of Mathematics of the Polish Academy of Sciences

Journal of Theoretical Probability, 2025, vol. 38, issue 3, 1-29

Abstract: Abstract We describe all Gaussian generating functionals on several easy quantum groups given by non-crossing partitions. This includes in particular the free unitary, orthogonal and symplectic quantum groups. We further characterize central Gaussian generating functionals and describe a centralization procedure yielding interesting (non-Gaussian) generating functionals.

Keywords: Gaussian functionals; Partition quantum groups; Quantum Lévy processes; Primary 46L53; Secondary 81R50 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-025-01425-w

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