Infinite curvature, quantum random walks, and Pitman's celebrated 2M-X theorem

par Prof. Reda Chhaibi

mardi 4 mars 2025, 14:00 → 15:00 Europe/Paris

The classical theorem by Pitman (1975) states that a Brownian motion minus twice its running infimum enjoys the Markov property. It has the same law as the norm of a 3-dimensional Brownian motion.

 

We start by recalling the long history of this theorem. In particular, we shall focus on the relationship to mathematical physics, where the theorem and its generalizations bridge random matrix theory and directed percolation.

Then we explain how Pitman's Theorem can be understood as a curvature interpolation between a flat regime and an infinite curvature regime.

 

In fact this story is the semi-classical limit of representation theoretic story. In the last section, we shall mention the relationship to quantum random walks, and the representation theory of quantum groups.

Based on joint work with F. Chapon

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