Random Walks and Heat Kernels on Graphs

Nonfiction, Science & Nature, Mathematics, Statistics, Science
Cover of the book Random Walks and Heat Kernels on Graphs by Martin T. Barlow, Cambridge University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Martin T. Barlow ISBN: 9781108124294
Publisher: Cambridge University Press Publication: February 23, 2017
Imprint: Cambridge University Press Language: English
Author: Martin T. Barlow
ISBN: 9781108124294
Publisher: Cambridge University Press
Publication: February 23, 2017
Imprint: Cambridge University Press
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Cambridge University Press

Cover of the book The Crime of Aggression by Martin T. Barlow
Cover of the book An Introduction to Japanese Society by Martin T. Barlow
Cover of the book Pragmatic Strategy by Martin T. Barlow
Cover of the book Racial and Ethnic Politics in American Suburbs by Martin T. Barlow
Cover of the book Cybercrime by Martin T. Barlow
Cover of the book A Realistic Theory of Law by Martin T. Barlow
Cover of the book Party Autonomy in Contractual Choice of Law in China by Martin T. Barlow
Cover of the book Chimpanzees of the Lakeshore by Martin T. Barlow
Cover of the book African Americans and the Pacific War, 1941–1945 by Martin T. Barlow
Cover of the book An Introduction to Genetics for Language Scientists by Martin T. Barlow
Cover of the book Human Trafficking and Slavery Reconsidered by Martin T. Barlow
Cover of the book The Urbanism of Exception by Martin T. Barlow
Cover of the book Making the Law of the Sea by Martin T. Barlow
Cover of the book Clinical Perspectives on Autobiographical Memory by Martin T. Barlow
Cover of the book Ancient Antioch by Martin T. Barlow
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy