Fusion coefficients and random walks in alcoves
Probability
2013-07-16 v1
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.
Cite
@article{arxiv.1307.3830,
title = {Fusion coefficients and random walks in alcoves},
author = {Manon Defosseux},
journal= {arXiv preprint arXiv:1307.3830},
year = {2013}
}