Probability on Trees and Networks

This book explores the relationship between the geometry of graphs and stochastic processes, covering percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, it emphasizes intuition and provides complete proofs and exercises. Recent developments, such as percolation on trees and Cayley graphs, uniform spanning forests, and connections to embedding in Hilbert space, are discussed.

Format: Paperback / softback
Publication date: 03 June 2021
Publisher: Cambridge University Press

In the late 1950s, a remarkable convergence of research communities emerged, linking the geometry of graphs to stochastic processes unfolding on these intricate networks. Over two decades in the making, this comprehensive book brings together a wealth of research in the field, encompassing a diverse range of topics such as percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two esteemed researchers, this text strikes a perfect balance between intuition and rigorous proof, offering comprehensive explanations accompanied by over 850 engaging exercises. The authors have played a pivotal role in many recent developments, including groundbreaking work on percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and the intricate connections between random walks on graphs and embedding in Hilbert space. This cutting-edge account of probability on networks stands as a vital resource for both graduate students and seasoned researchers, providing a comprehensive and up-to-date exploration of this dynamic and rapidly evolving field.

Weight: 1338g
Dimension: 178 x 253 x 42 (mm)
ISBN-13: 9781108732727