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Random walk on a building of type Ãr and brownian motion of the Weyl chamber

Bruno Schapira (2009)

Annales de l'I.H.P. Probabilités et statistiques

In this paper we study a random walk on an affine building of type Ãr, whose radial part, when suitably normalized, converges toward the brownian motion of the Weyl chamber. This gives a new discrete approximation of this process, alternative to the one of Biane (Probab. Theory Related Fields89 (1991) 117–129). This extends also the link at the probabilistic level between riemannian symmetric spaces of the noncompact type and their discrete counterpart, which had been previously discovered by Bougerol...

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