Probability on Trees & Networks by Lyons & Peres
Probability on Trees & Networks - Table of Contents
- 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
What You Will Learn in Probability on Trees & Networks
Probability on Trees and Networks by Russell Lyons and Yuval Peres is a definitive, world-renowned monograph exploring the rich interactions between probability theory, harmonic analysis, geometry, and graph theory. Designed for advanced graduate students and research mathematicians, this foundational text breaks down complex topics like reversible Markov chains, electrical networks, uniform spanning trees, percolation phase transitions, and renewal processes on trees into precise, self-contained chapters.
Perfect for doctoral candidates and academic researchers in spatial probability, statistical mechanics, geometric group theory, and theoretical computer science, this comprehensive book connects classic probabilistic intuition with powerful algebraic and geometric methods. Lyons and Peres systematically analyze how graph geometry influences probabilistic phenomena, including speed of random walks, capacity theory, and cutsets. Whether you are studying infinite networks, boundary theory, or determinantal point processes, this text provides a deep, structured roadmap through every chapter.
Recognized globally for its encyclopedic scope, mathematical beauty, and rigorous detail, it remains one of the best probability on graphs books pdf available for high-level study. It systematically equips readers with advanced analytical frameworks for mastering modern probability on infinite networks with confidence.
Book Details & Specifications
Title:
Probability on Trees & Networks by Lyons & Peres
Publisher:
Cambridge University Press
Year:
2016
Pages:
716
Type:
PDF
Language:
English
ISBN-10 #:
B01N7DKTQU
ISBN-13 #:
978-1316787571
License:
University Educational Resource
Amazon:
Amazon
About the Author: Russell Lyons and Yuval Peres
The author Russell Lyons and Yuval Peres
are leading mathematicians specializing in probability and stochastic processes. Russell Lyons was born in "New York, USA", earned his "Ph.D. from UC Berkeley", and is a professor at "Indiana University". Yuval Peres was born in "Jerusalem, Israel", also earned his "Ph.D. from UC Berkeley", and teaches at "UC Berkeley". Both have made significant contributions to mathematical research and education in random structures and networks. Their expertise includes "Probability Theory", "Stochastic Processes", "Random Walks", "Graph Theory", and "Trees and Networks". Through their book "Probability on Trees & Networks", Lyons and Peres provide a clear, modern introduction to probabilistic methods applied to trees, networks, and complex systems, making advanced mathematical concepts accessible to students and researchers alike.
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