Introduction

Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs.

Overview

This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks.

Authors and Approach

Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises.

Recent Developments

Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space.

Target Audience

This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.