How about these two books for a start?

Tullio Ceccherini-Silberstein, Fabio Scarabotti, and Filippo Tolli. Harmonic analysis on finite groups. Representation theory, Gelfand pairs and Markov chains. Cambridge Studies in Advanced Mathematics 108. Cambridge: Cambridge University Press, 2008.

Persi Diaconis. Group representations in probability and statistics. IMS Lecture Notes-Monograph Series, 11. Hayward, CA: Institute of Mathematical Statistics, 1988.