Probability on Trees and Networks

ISBN-13: 9781108732727 / Angielski / Miękka / 2021

Russell Lyons; Yuval Peres

Opis

Consolidating over sixty years of research, this authoritative account of probability on networks is indispensable to anyone in the field.

Recenzje

'This long-awaited book, a project that started in 1993, is bound to be the main reference in the fascinating field of probability on trees and weighted graphs. The authors are the leading experts behind the tremendous developments experienced in the subject in recent decades, where the underlying networks evolved from classical lattices to general graphs … This pedagogically written book is a marvelous support for several courses on topics from combinatorics, Markov chains, geometric group theory, etc., as well as on their inspiring relationships. The wealth of exercises (with comments provided at the end of the book) will enable students and researchers to check their understanding of this fascinating mathematics.' Laurent Miclo, MathSciNet

Spis treści

1. Some highlights; 2. Random walks and electric networks; 3. Special networks; 4. Uniform spanning trees; 5. Branching processes, second moments, and percolation; 6. Isoperimetric inequalities; 7. Percolation on transitive graphs; 8. The mass-transport technique and percolation; 9. Infinite electrical networks and Dirichlet functions; 10. Uniform spanning forests; 11. Minimal spanning forests; 12. Limit theorems for Galton–Watson processes; 13. Escape rate of random walks and embeddings; 14. Random walks on groups and Poisson boundaries; 15. Hausdorff dimension; 16. Capacity and stochastic processes; 17. Random walks on Galton–Watson trees.