ATMW Probabability and Representation Theory (2016)

Venue: The Institute of Mathematical Sciences, Chennai
Date:  7th to 12th March 2016


Name: Professor Arvind Ayyer Professor K N Raghavan
Mailing Address: Assistant Professor
Department of Mathematics
Indian Institute of Science
Bangalore 560 012
Professor H
Mathematics Group
The Institute of Mathematical Sciences,
CIT Campus, Taramani
Chennai 600 113
Email: arvind at knr at

Since the pioneering work of Diaconis and Shahshahani on generating random permutations using transpositions in 1981, representation theory has become an important tool in understanding random walks on finite groups. We will study certain natural random walk models on the symmetric group in increasing order of difficulty: random transpositions, top-to-random shuffle, Tsetlin library, random-to-random shuffle. In these models, one prescribes a probabilistic rule that describes what the possible permutations are at time n+1 if one has a certain permutation at time n (time is taken to be discrete). For each model, we will understand how a random permutation looks like after a long time and how long it takes for the distribution to reach stationarity. The first three models are well-studied; we will develop our understanding of the theory by working through them. In the end, we will discuss the fourth model, where some of the same questions remain open. Very recently (on 29th September 2015) a preprint has been posted to the arXiv announcing proofs of the eigenvalue conjectures in this model.