Random braids and random walks on finite groups

TL;DR

This paper investigates the properties of random walks on finite groups and applies these findings to analyze the expected braid length and component number in a model of random braids derived from Coxeter group elements.

Contribution

It introduces a novel approach linking random walks on Coxeter groups to properties of random braids, providing new insights into braid length and component expectations.

Findings

Derived limiting expectations for braid length and component number

Established connections between random walks on Coxeter groups and braid properties

Provided a probabilistic framework for analyzing braid closures

Abstract

In this paper, we study properties of random walks on finite groups and later use them to obtain the limiting braid length expectation and component number of braid closure in a model of random braids, which is constructed by lifting elements of random walk on a Coxeter group to a braid group.