Random walks and heat kernels on graphs /

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Bibliographic Details
Author / Creator:Barlow, M. T.
Imprint:©2017
Cambridge : Cambridge University Press, [2017]
Description:1 online resource
Language:English
Series:London Mathematical Society lecture note series ; 438
London Mathematical Society lecture note series ; 438.
Subject:
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/13454746
Hidden Bibliographic Details
ISBN:9781108125604
1108125603
9781107674424
1107674425
9781107415690
1107415691
Notes:Includes bibliographical references and index.
Print version record.
Summary: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 Poincar 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.
Other form:Print version: Barlow, M.T. Random walks and heat kernels on graphs. Cambridge : Cambridge University Press, [2017] 9781107674424
Standard no.:40026971296