A Survey of Results on Random Random Walks on Finite Groups
  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. 
Martin Hildebrand