Harmonic Functions and Random Walks on Groups

‘This is a wonderful introduction to random walks and harmonic functions on finitely generated groups. The focus is the characterization of Choquet-Deny groups. The text offers a balanced treatment of well-chosen topics involving probabilistic and algebraic arguments presented with accuracy and care. The rich list of exercises with solutions will certainly help and entertain the reader.’ Laurent Saloff-Coste, Cornell University‘Written by a leading expert in the field, this book explores the fundamental results of this captivating area at the boundary of probability and geometric group theory—an essential read for aspiring young researchers.’ Hugo Duminil-Copin, Institut des Hautes Études Scientifiques and Université de Genève‘This voluminous book is a substantial contribution to the state of the art of random walk theory, which has evolved enormously in the last decades. A broad initial part on the basics is guided by numerous exercises. The core chapters are on the relation between harmonic functions for random walks and the structure of the underlying groups, in particular growth. The final highlight is a modern exposition of Gromov’s theorem on polynomial growth and its strong interplay with the topics of the book’s title.’ Wolfgang Woess, Technische Universität Graz

Ariel Yadin is Professor in the Department of Mathematics at Ben-Gurion University of the Negev. His research is focused on the interplay between random walks and the geometry of groups. He has taught a variety of courses on the subject, and has been part of a new wave of investigation into the structure of spaces of unbounded harmonic functions on groups.