Random Walks on Reductive Groups

Introduction.- Part I The Law of Large Numbers.- Stationary measures.- The Law of Large Numbers.- Linear random walks.- Finite index subsemigroups.- Part II Reductive groups.- Loxodromic elements.- The Jordan projection of semigroups.- Reductive groups and their representations.- Zariski dense subsemigroups.- Random walks on reductive groups.- Part III The Central Limit Theorem.- Transfer operators over contracting actions.- Limit laws for cocycles.- Limit laws for products of random matrices.- Regularity of the stationary measure.- Part IV The Local Limit Theorem.- The Spectrum of the complex transfer operator.- The Local limit theorem for cocycles.- The local limit theorem for products of random matrices.- Part V Appendix.- Convergence of sequences of random variables.- The essential spectrum of bounded operators.- Bibliographical comments.

"Benoist and Quint have written an excellent text, one that will surely become a standard reference to introduce students to the fascinating nonabelian extension of the now-classical study of random walks. ... I congratulate the authors on their well-written and timely offering, and strongly recommend that libraries order a copy of this excellent text!" (Tushar Das, MAA Reviews, November, 2017)

"This book is an exposition of the tools and perspectives needed to reach the current frontier of research in the field of random matrix products... This is a technical subject, drawing on tools from a diverse range of topics... The authors take time to explain everything at a reasonable pace." (Radhakrishnan Nair, Mathematical Reviews)

 "This reviewer does not hesitate to consider this book as exceptional." (Marius Iosifescu, zbMATH, 1366.60002)