Cutoff Phenomenon and Limiting Profile of a Random Walk on the Symmetric Group

TL;DR

This paper reviews representation theoretic methods for analyzing the mixing times of random walks on finite groups, highlighting classical and recent results on card shuffles.

Contribution

It provides an overview of techniques and recent advancements in understanding the cutoff phenomenon for random walks on symmetric groups.

Findings

Analysis of the cutoff phenomenon in card shuffles

Recent improvements on mixing time bounds

Application of representation theory to finite groups

Abstract

We present an overview of the representation theoretic techniques used to study the mixing times of random walks on finite groups. We focus on the card shuffle studied by Diaconis and Shahshahani in the 1980s and a recent improvement on their result by Teyssier