From Pitman's theorem to crystals

Philippe Biane (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

We describe an extension of Pitman's theorem on Brownian motion and the three dimensional Bessel process to several dimensions. We show how this extension is suggested by considering a random walk on a noncommutative space, and is connected with crystals and Littelmann paths.

Domaines: Probabilités [math.PR]

Philippe Biane. From Pitman's theorem to crystals. J.-P. Bourguignon, M. Kotani, Y. Maeda, N. Tose. Noncommutativity and Singularities, 55, Mathematical Society of Japan, Kinokuniya, pp.1-13, 2009, Advanced Studies in Pure Mathematics. ⟨hal-00846322⟩