Random Walks and Heat Kernels on Graphs
eBook - PDF

Random Walks and Heat Kernels on Graphs

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

Random Walks and Heat Kernels on Graphs

About this book

This introduction to random walks on infinite graphs gives particular emphasis to graphs with polynomial volume growth. It offers an overview of analytic methods, starting with the connection between random walks and electrical resistance, and then proceeding to study the use of isoperimetric and Poincaré inequalities. The book presents rough isometries and looks at the properties of a graph that are stable under these transformations. Applications include the 'type problem': determining whether a graph is transient or recurrent. The final chapters show how geometric properties of the graph can be used to establish heat kernel bounds, that is, bounds on the transition probabilities of the random walk, and it is proved that Gaussian bounds hold for graphs that are roughly isometric to Euclidean space. Aimed at graduate students in mathematics, the book is also useful for researchers as a reference for results that are hard to find elsewhere.

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Yes, you can access Random Walks and Heat Kernels on Graphs by Martin T. Barlow in PDF and/or ePUB format, as well as other popular books in Mathematics & Probability & Statistics. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Series page
  3. Title page
  4. Copyright page
  5. Dedication
  6. Contents
  7. Preface
  8. 1 Introduction
  9. 2 Random Walks and Electrical Resistance
  10. 3 Isoperimetric Inequalities and Applications
  11. 4 Discrete Time Heat Kernel
  12. 5 Continuous Time Random Walks
  13. 6 Heat Kernel Bounds
  14. 7 Potential Theory and Harnack Inequalities
  15. Appendix
  16. References
  17. Index