Fusion coefficients and random walks in alcoves

Manon Defosseux (1)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

We point out a connection between fusion coefficients and random walks in a fixed level alcove associated to the root system of an affine Lie algebra and use this connection to solve completely the Dirichlet problem on such an alcove for a large class of simple random walks. We establish a correspondence between the hypergroup of conjugacy classes of a compact Lie group and the fusion hypergroup. We prove that a random walk in an alcove, obtained with the help of fusion coefficients, converges, after a proper normalization, towards the radial part of a Brownian motion on a compact Lie group.

Domaines: Probabilités [math.PR]

Manon Defosseux. Fusion coefficients and random walks in alcoves. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2014. ⟨hal-00844322⟩