Isotropic Random Walks on Affine Buildings
نویسنده
چکیده
Recently, Cartwright and Woess [5] provided a detailed analysis of isotropic random walks on the vertices of thick affine buildings of type Ãn. Their results generalise results of Sawyer [18] where homogeneous trees are studied (these are Ã1 buildings), and Lindlbauer and Voit [9], where Ã2 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 Ãn case.
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