From Pitman's theorem to crystals

Abstract : 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.
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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⟩

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