The barycenter in free nilpotent Lie groups and its application to iterated-integrals signatures

Marianne Clausel, Joscha Diehl, Raphael Mignot +3

We establish the well-definedness of the barycenter (in the sense of Buser and Karcher) for every integrable measure on the free nilpotent Lie group of step $L$ (over $\mathbb{R}^d…