[Math] Easier reference for material like Diaconis’s “Group representations in probability and statistics”

Question

I'm teaching a class on the representation theory of finite groups at the advanced undergrad level. One of the things I'd like to talk about, or possibly have a student do any independent project on is applications of finite groups in statistics and data analysis. Unfortunately, the only book I know on the subject is Persi Diaconis's Group representations in probability and statistics, which is lovely but nowhere close to the level that I would expect an undergrad to read (or for that matter, anyone from a field outside math). Are there any books or articles people know of which provide a gentler introduction?

Answer 1

I have a chapter on this in my book Steinberg - Representation theory of finite groups. Sorry for the self promotion. It is intended for advanced undergrads. I basically focus on the abelian case, giving the upper bound lemma on convergence rates and the description of the eigenvalues for this case only. I do one explicit computation (I don't have the book in front of me right now, but I think I do it for the lazy random walk on the hypercube). Also, if memory serves there is an exercise on what to do if the probability measure is constant on conjugacy classes for non abelian groups,, but maybe that was in the section on eigenvalues of Cayley graphs.)

An alternative is Harmonic Analysis on Finite Groups Representation Theory, Gelfand Pairs and Markov Chain by Tullio Ceccherini-Silberstein, Fabio Scarabotti, andFilippo Tolli, but I find it no easier than Diaconis except that it may expect more of an algebra background than a probability background.