Fusion coefficients and random walks in alcoves

Abstract : 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.
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  • HAL Id : hal-00844322, version 1
  • ARXIV : 1307.3830

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

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