A number of papers have examined various aspects of “random random walks” on finite groups; the purpose of this article is to provide a survey of this work and to show, bring together, and discuss some of the arguments and results in this work. This article also provides a number of exercises. Some exercises involve straightforward computations; others involve proving details in proofs or extending results proved in the article. This article also describes some problems for further study.
"A survey of results on random random walks on finite groups." Probab. Surveys 2 33 - 63, 2005. https://doi.org/10.1214/154957805100000087