Harmonic Analysis on Finite Groups

Representation Theory, Gelfand Pairs and Markov Chains

Harmonic Analysis on Finite Groups

Starting from a few concrete problems such as random walks on the discrete circle and the finite ultrametric space, this book develops the necessary tools for the asymptotic analysis of these processes. Its topics range from the basic theory needed for students new to this area, to advanced topics such as the theory of Green’s algebras, the complete analysis of the random matchings, and a presentation of the presentation theory of the symmetric group. This self-contained, detailed study culminates with case-by-case analyses of the cut-off phenomenon discovered by Persi Diaconis.


"This book is, as far as I know, the first treatise fully devoted to finite Gel'fand pairs and their applications to probability and combinatories. ... It has lots of worked-out examples, and dozens of exercises (the solutions of which can be found in Appendix 2)."
Alain Valette, Mathematical Reviews

"This is the perfect group theory resource for probability theory students."
D.V. Feldman, University of New Hampshire for Choice Magazine