Probability on Trees & Networks by Lyons & Peres

Book 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

About this book :-
"Probability on Trees & Networks" by Russell Lyons and Yuval Peres is a clear and engaging guide to understanding how probability works in structured systems. The book explores "Probability on Trees", showing how random processes behave on tree-like structures and networks. It starts with basic concepts in "Graph Theory" and probability, gradually introducing more advanced topics such as random walks, percolation, and harmonic functions. Readers learn how mathematical tools can describe complex network behaviors in social systems, computer science, and physical models. The middle sections focus on advanced methods, including "Markov Chains", potential theory, and stochastic processes on infinite trees and networks. The authors explain how these concepts help analyze network connectivity, recurrence, and transience, providing insight into how random events propagate through networks. Practical examples and exercises make abstract concepts more tangible, helping readers apply the theory to real-world systems and understand phenomena such as information flow, epidemic spread, and network reliability. The final chapters connect theory with applications, demonstrating how probability theory on structured graphs underlies many areas of modern research. By combining rigorous mathematics with intuitive explanations, the book is ideal for graduate students, researchers, and professionals in "Networks", applied mathematics, and theoretical computer science. It serves as both a reference and a learning tool for anyone studying the behavior of complex random systems.

Book Detail :-
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 Author :-
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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