Introduction to analysis on graphs
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 r…
Read More ↓Title Statements
- Full title :Introduction to analysis on graphs / Alexander Grigor'yan.
Summary
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.--
Read More ↓Edition Statements
- Publication Date:©2018
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:Providence, Rhode Island
- Language:eng
- Publication Date:©2018
The Physical Object
- Description:viii, 150 pages : : illustrations ; : 26 cm.
Edition Identifiers
- ISBN:147044397X, 9781470443979
- oclc:on1022978581
- LC Classification:QA166
- Dewey Decimal:511/.5
Table of Contents
The Laplace operator on graphs -- Spectral properties of the Laplace operator -- Geometric bounds for the eigenvalues -- Eigenvalues on infinite graphs -- Estimates of the heat kernel -- The type problem -- Exercises.
Read More ↓Subjects
Writers
More from this Series
No reviews yet. Be the first to rate this work.
Rate & Review