- 240 pages
- English
- PDF
- 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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Information
Table of contents
- Cover
- Series page
- Title page
- Copyright page
- Dedication
- Contents
- Preface
- 1 Introduction
- 2 Random Walks and Electrical Resistance
- 3 Isoperimetric Inequalities and Applications
- 4 Discrete Time Heat Kernel
- 5 Continuous Time Random Walks
- 6 Heat Kernel Bounds
- 7 Potential Theory and Harnack Inequalities
- Appendix
- References
- Index
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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 1.5 million books available in our catalogue for you to explore.