# Limit profile for random transpositions

## TL;DR

This paper improves a mathematical tool to better analyze how quickly random transpositions mix to a uniform distribution, enhancing understanding of their convergence behavior.

## Contribution

It introduces an improved upper bound lemma for analyzing the limit profile of random transpositions, refining previous methods.

## Key findings

- Enhanced bounds for the mixing time of random transpositions
- More precise estimates of convergence to stationarity
- Application of the improved lemma to classical random transposition models

## Abstract

We present an improved version of Diaconis' upper bound lemma, which is used to compute the limiting value of the distance to stationarity. We then apply it to random transpositions studied by Diaconis and Shahshahani.