Probability on Trees and Networks
eBook - PDF

Probability on Trees and Networks

  1. 725 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Probability on Trees and Networks

About this book

Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. 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. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. 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. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.

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Information

Publisher
Cambridge University Press
Year
2017
Print ISBN
9781107160156
eBook ISBN
9781316786611
Topic
Mathematics
Subtopic
Probability & Statistics
Index
Mathematics

Table of contents

  1. Cover
  2. Half title
  3. Dedication
  4. Series
  5. Title
  6. Copyright
  7. Contents
  8. Preface
  9. Chapter 1: Some Highlights
  10. Chapter 2: RandomWalks and Electric Networks
  11. Chapter 3: Special Networks
  12. Chapter 4: Uniform Spanning Trees
  13. Chapter 5: Branching Processes, Second Moments, and Percolation
  14. Chapter 6: Isoperimetric Inequalities
  15. Chapter 7: Percolation on Transitive Graphs
  16. Chapter 8: The Mass-Transport Technique and Percolation
  17. Chapter 9: Infinite Electrical Networks and Dirichlet Functions
  18. Chapter 10: Uniform Spanning Forests
  19. Chapter 11: Minimal Spanning Forests
  20. Chapter 12: Limit Theorems for Galton-Watson Processes
  21. Chapter 13: Escape Rate of RandomWalks and Embeddings
  22. Chapter 14: RandomWalks on Groups and Poisson Boundaries
  23. Chapter 15: Hausdorff Dimension
  24. Chapter 16: Capacity and Stochastic Processes
  25. Chapter 17: RandomWalks on Galton-Watson Trees
  26. Comments on Exercises
  27. Bibliography
  28. Glossary of Notation
  29. Index

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Yes, you can access Probability on Trees and Networks by Russell Lyons,Yuval Peres in PDF and/or ePUB format, as well as other popular books in Mathematics & Probability & Statistics. We have over 1.5 million books available in our catalogue for you to explore.