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Isotropic random walks on affine buildings

James Parkinson — 2007

Annales de l’institut Fourier

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 ${\tilde{A}}_{n}$ buildings are studied, Lindlbauer and Voit where ${\tilde{A}}_{2}$ buildings are studied, and Sawyer where homogeneous trees are studied (these are ${\tilde{A}}_{1}$ buildings).

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