Random Walks On Finite Groups - Card Shuffling

Mentor: Evita Nestoridi

One of the main questions concerning a random walk on a finite group is finding the order of the mixing time of the walk. In particular, in card shuffling we are really interested in finding out how many shuffles are required to get the deck "perfectly" shuffled. In this project, we are going to learn techniques of bounding the mixing time and play with a lot of examples. We will try to actually solve particular problems-examples either from card shuffling or from a group of matrices over a finite field (or perhaps another finite group that we might find interesting) and ideally come up with new techniques for bounding the mixing time.