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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 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).

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