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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 , 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 ( (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...

Poisson boundary of triangular matrices in a number field

Bruno Schapira — 2009

Annales de l’institut Fourier

The aim of this note is to describe the Poisson boundary of the group of invertible triangular matrices with coefficients in a number field. It generalizes to any dimension and to any number field a result of Brofferio concerning the Poisson boundary of random rational affinities.

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