Buildings, groups of Lie type, and random walks

TL;DR

This paper surveys the theory of random walks on buildings and related groups of Lie type, highlighting combinatorial foundations and limit theorems for these stochastic processes.

Contribution

It provides a comprehensive overview connecting Coxeter systems, buildings, and random walks, emphasizing new limit theorems for groups of Lie type and Kac-Moody groups.

Findings

Limit theorems for random walks on buildings

Connections between Coxeter systems and stochastic processes

Survey of random walk behavior on algebraic groups

Abstract

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 systems and buildings, taking a largely combinatorial perspective. We then survey the theory of random walks on buildings, and show how this theory leads to limit theorems for random walks on the associated groups.