Motoko Kotani 
Discrete Geometric Analysis [PDF ebook] 

This book is a collection of papers from the proceedings of the first symposium of the Japan Association for Mathematical Sciences. Topics covered center around problems of geometric analysis in relation to heat kernels, random walks, and Poisson boundaries on discrete groups, graphs, and other combinatorial objects. The material is suitable for graduate students and research mathematicians interested in heat kernels and random works on groups and graphs.