Introduction to Analysis on Graphs (University Lecture Series) - Softcover

Alexander Grigor'yan (author)

 
9781470443979: Introduction to Analysis on Graphs (University Lecture Series)
Softcover
ISBN 10: 147044397X ISBN 13: 9781470443979
Publisher: American Mathematical Society, 2018

Synopsis

A central object of this book is the discrete Laplace operator on finite and infinite graphs. The eigenvalues of the discrete Laplace operator have long been used in graph theory as a convenient tool for understanding the structure of complex graphs. They can also be used in order to estimate the rate of convergence to equilibrium of a random walk (Markov chain) on finite graphs. For infinite graphs, a study of the heat kernel allows to solve the type problem-a problem of deciding whether the random walk is recurrent or transient.

This book starts with elementary properties of the eigenvalues on finite graphs, continues with their estimates and applications, and concludes with heat kernel estimates on infinite graphs and their application to the type problem. The book is suitable for beginners in the subject and accessible to undergraduate and graduate students with a background in linear algebra I and analysis I. It is based on a lecture course taught by the author and includes a wide variety of exercises. The book will help the reader to reach a level of understanding sufficient to start pursuing research in this exciting area.

"synopsis" may belong to another edition of this title.

About the Author

Alexander Grigor'yan, University of Bielefeld, Germany.

"About this title" may belong to another edition of this title.

Publisher
American Mathematical Society
Publication date
2018
Language
English
ISBN 10 
147044397X
ISBN 13 
9781470443979
Binding
Paperback
Number of pages
168