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 buildings are studied, Lindlbauer and Voit where buildings are studied, and Sawyer where homogeneous trees are studied (these are buildings).
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 , de Lindlbauer et Voit sur les immeubles de type et de Sawyer sur les arbres homogènes (qui sont des immeubles de type ).
Keywords: Affine buildings, random walks, Macdonald spherical functions
Mot clés : immeubles affines, marche aléatoire, fonctions sphériques de Macdonald
Parkinson, James 1
@article{AIF_2007__57_2_379_0, author = {Parkinson, James}, title = {Isotropic random walks on affine buildings}, journal = {Annales de l'Institut Fourier}, pages = {379--419}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {57}, number = {2}, year = {2007}, doi = {10.5802/aif.2262}, mrnumber = {2310945}, zbl = {1177.60046}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2262/} }
TY - JOUR AU - Parkinson, James TI - Isotropic random walks on affine buildings JO - Annales de l'Institut Fourier PY - 2007 SP - 379 EP - 419 VL - 57 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2262/ DO - 10.5802/aif.2262 LA - en ID - AIF_2007__57_2_379_0 ER -
%0 Journal Article %A Parkinson, James %T Isotropic random walks on affine buildings %J Annales de l'Institut Fourier %D 2007 %P 379-419 %V 57 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2262/ %R 10.5802/aif.2262 %G en %F AIF_2007__57_2_379_0
Parkinson, James. Isotropic random walks on affine buildings. Annales de l'Institut Fourier, Volume 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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