Regular sequences and random walks in affine buildings

Parkinson, James; Woess, Wolfgang

Annales de l'Institut Fourier, Tome 65 (2015) no. 2, pp. 675-707.

On donne la définition et des caractérisations de suites régulières dans les immeubles affines. Ce faisant, on obtient l’analogue $p$-adique du travail fondamental de Kaimanovich sur les suites régulières dans les espaces symétriques. Comme application, nous démontrons des théorèmes limite pour des marches aléatoires dans les immeubles affines et leurs groupes d’automorphismes.

We define and characterise regular sequences in affine buildings, thereby giving the $p$-adic analogue of the fundamental work of Kaimanovich on regular sequences in symmetric spaces. As applications we prove limit theorems for random walks on affine buildings and their automorphism groups.

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