PreprintIsotropic Random Walks on Affine BuildingsJ. ParkinsonAbstractRecently, Cartwright and Woess provided a detailed analysis of isotropic random walks on the vertices of thick affine buildings of type \tilde{A}_{n}. Their results generalise results of Sawyer, where homogeneous trees are studied (these are \tilde{A}_{1} buildings), and Lindlbauer and Voit, where \tilde{A}_{2} buildings are studied. 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, thus providing a broad generalisation of the \tilde{A}_{n} case.Keywords: Affine buildings, random walks, Macdonald spherical functions. AMS Subject Classification: Primary 20E42; secondary (60G50 33D52).
