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

Bruno Schapira

Annales de l'I.H.P. Probabilités et statistiques (2009)

  • Volume: 45, Issue: 2, page 289-301
  • ISSN: 0246-0203

Abstract

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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 and Jeulin in rank one (C. R. Acad. Sci. Paris Sér. I Math.333 (2001) 785–790). The main ingredients of the proof are a combinatorial formula on the building and the estimate of the transition density proved in Anker et al. (2006).

How to cite

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Schapira, Bruno. "Random walk on a building of type Ãr and brownian motion of the Weyl chamber." Annales de l'I.H.P. Probabilités et statistiques 45.2 (2009): 289-301. <http://eudml.org/doc/78024>.

@article{Schapira2009,
abstract = {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 and Jeulin in rank one (C. R. Acad. Sci. Paris Sér. I Math.333 (2001) 785–790). The main ingredients of the proof are a combinatorial formula on the building and the estimate of the transition density proved in Anker et al. (2006).},
author = {Schapira, Bruno},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {random walk; affine building; root systems; GUE process; Brownian motion},
language = {eng},
number = {2},
pages = {289-301},
publisher = {Gauthier-Villars},
title = {Random walk on a building of type Ãr and brownian motion of the Weyl chamber},
url = {http://eudml.org/doc/78024},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Schapira, Bruno
TI - Random walk on a building of type Ãr and brownian motion of the Weyl chamber
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2009
PB - Gauthier-Villars
VL - 45
IS - 2
SP - 289
EP - 301
AB - 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 and Jeulin in rank one (C. R. Acad. Sci. Paris Sér. I Math.333 (2001) 785–790). The main ingredients of the proof are a combinatorial formula on the building and the estimate of the transition density proved in Anker et al. (2006).
LA - eng
KW - random walk; affine building; root systems; GUE process; Brownian motion
UR - http://eudml.org/doc/78024
ER -

References

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