1,589 research outputs found
Isotropic random walks on affine buildings
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.Comment: To appear in Annales de l'Institut Fourie
Buildings and Hecke algebras
This paper investigates the connections between buildings and Hecke algebras
through the combinatorial study of two algebras spanned by averaging operators
on buildings. As a consequence we obtain a geometric and combinatorial
description of certain Hecke algebras, and in particular of the Macdonald
spherical functions and the center of affine Hecke algebras. The results of
this paper are used in later work to study spherical harmonic analysis on
affine buildings, and to study isotropic random walks on affine buildings
Regular sequences and random walks in affine buildings
We define and characterise regular sequences in affine buildings, thereby
giving the "-adic analogue" of the fundamental work of Kaimanovich. As
applications we prove limit theorems for random walks on affine buildings and
their automorphism groups
Automorphisms and opposition in twin buildings
We show that every automorphism of a thick twin building interchanging the
halves of the building maps some residue to an opposite one. Furthermore we
show that no automorphism of a locally finite 2-spherical twin building of rank
at least 3 maps every residue of one fixed type to an opposite. The main
ingredient of the proof is a lemma that states that every duality of a thick
finite projective plane admits an absolute point, i.e., a point mapped onto an
incident line. Our results also hold for all finite irreducible spherical
buildings of rank at least 3, and as a consequence we deduce that every
involution of a thick irreducible finite spherical building of rank at least 3
has a fixed residue
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