Regular sequences and random walks in affine buildings

TL;DR

This paper introduces regular sequences in affine buildings, providing a $p$-adic analogue to classical work, and applies this to establish limit theorems for random walks on these structures and their automorphism groups.

Contribution

It defines and characterizes regular sequences in affine buildings, extending fundamental work to the $p$-adic setting, and proves related limit theorems for random walks.

Findings

Characterization of regular sequences in affine buildings

Limit theorems for random walks on affine buildings

Applications to automorphism groups of affine buildings

Abstract

We define and characterise regular sequences in affine buildings, thereby giving the "$p$-adic analogue" of the fundamental work of Kaimanovich. As applications we prove limit theorems for random walks on affine buildings and their automorphism groups.