no. 2
Isotropic random walks on affine buildings
[Marches aléatoires isotropes sur les immeubles affines]
Parkinson, James1
1 University of Sydney School of Mathematics and Statistics F07 Sydney NSW 2006 (Australia)
Annales de l'Institut Fourier, Tome 57 (2007) no. 2, pp. 379-419.

Dans cet article, nous utilisons les techniques de l’analyse harmonique sphérique pour démontrer un théorème local limite, un théorème sur la vitesse de fuite et un théorème central limite pour les marches aléatoires isotropes sur des immeubles affines épais arbitraires de type irréductible. Cela généralise des résultats de Cartwright et Woess sur les immeubles de type A ˜ n , de Lindlbauer et Voit sur les immeubles de type A ˜ 2 et de Sawyer sur les arbres homogènes (qui sont des immeubles de type A ˜ 1 ).

In this paper we apply techniques of spherical harmonic analysis to prove a local limit theorem, a rate of escape theorem, and a central limit theorem for isotropic random walks on arbitrary thick regular affine buildings of irreducible type. This generalises results of Cartwright and Woess where A ˜ n buildings are studied, Lindlbauer and Voit where A ˜ 2 buildings are studied, and Sawyer where homogeneous trees are studied (these are A ˜ 1 buildings).

DOI : 10.5802/aif.2262
Classification : 20E42, 60G50, 33D52
Keywords: Affine buildings, random walks, Macdonald spherical functions
Mot clés : immeubles affines, marche aléatoire, fonctions sphériques de Macdonald

Parkinson, James 1

1 University of Sydney School of Mathematics and Statistics F07 Sydney NSW 2006 (Australia) 
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Parkinson, James. Isotropic random walks  on affine buildings. Annales de l'Institut Fourier, Tome 57 (2007) no. 2, pp. 379-419. doi : 10.5802/aif.2262. https://aif.centre-mersenne.org/articles/10.5802/aif.2262/

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