Random Walks and Heat Kernels on Graphs (London Mathematical Society Lecture Note Series 438)

Barlow, Martin T

ISBN 10: 1107674425 / ISBN 13: 9781107674424

Published by Cambridge University Press, 2017

About this Item

Firm, square and tight with strong joints and sharp corners, just a non-text page stamped 'damaged' due to some hardly noticeable shelf wear. Despite such this book is actually in nearly condition: fresh, crisp and clean with no defects. Thus a nice copy in great shape offered for sale at a bargain price.

Seller Inventory # 115602

Bibliographic Details

• Title: Random Walks and Heat Kernels on Graphs (London Mathematical Society Lecture Note Series 438)
• Publisher: Cambridge University Press
• Publication Date: 2017
• Language: English
• ISBN 10: 1107674425
• ISBN 13: 9781107674424
• Binding: Paperback
• Edition: First Edition.
• Condition: Like New

About this title

Synopsis

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.

About the Author

Martin T. Barlow is Professor in the Mathematics Department at the University of British Columbia. He was one of the founders of the mathematical theory of diffusions on fractals, and more recently has worked on random walks on random graphs. He gave a talk at the International Congress of Mathematicians (ICM) in 1990, and was elected a Fellow of the Royal Society of Canada in 1998 and a Fellow of the Royal Society in 2005. He is the winner of the Jeffrey-Williams Prize of the Canadian Mathematical Society and the CRM-Fields-PIMS Prize of the three Canadian mathematics institutes (the Centre de recherches mathématiques, the Fields Institute, and the Pacific Institute for the Mathematical Sciences).