16 citations · 30 across the 18 of their papers we have counts for
5 papers · 1 filter
Buildings, groups of Lie type, and random walks
J. Parkinson
In this paper we survey the theory of random walks on buildings and associated groups of Lie type and Kac-Moody groups. We begin with an introduction to the theory of Coxeter syste…
Asymptotic entropy of random walks on Fuchsian buildings and Kac-Moody groups
Lorenz A. Gilch, Sebastian Müller, James Parkinson
In this article we prove existence of the asymptotic entropy for isotropic random walks on regular Fuchsian buildings. Moreover, we give formulae for the asymptotic entropy, and pr…
Regular sequences and random walks in affine buildings
James Parkinson, Wolfgang Woess
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 theo…
A local limit theorem for random walks on the chambers of buildings
James Parkinson, Bruno Schapira
In this paper we outline an approach for analysing random walks on the chambers of buildings. The types of walks that we consider are those which are well adapted to the structure…
Isotropic random walks on affine buildings
James Parkinson
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…