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Introduction to analysis on graphs

Author: A Grigoryan
Publisher: Providence, Rhode Island : American Mathematical Society, [2018]
Series: University lecture series (Providence, R.I.), 71.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Anybody who has ever read a mathematical text of the author would agree that his way of presenting complex material is nothing short of marvelous. This new book showcases again the author's unique ability of presenting challenging topics in a clear and accessible manner, and of guiding the reader with ease to a deep understanding of the subject. --Matthias Keller, University of Potsdam A central object of this book  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Grigor'yan, Alexander.
Introduction to analysis on graphs.
Providence, Rhode Island : American Mathematical Society, [2018]
(DLC) 2018001105
(OCoLC)1022978581
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: A Grigoryan
ISBN: 9781470448554 1470448556
OCLC Number: 1050362822
Description: 1 online resource.
Contents: Cover; Title page; Preface; Chapter 1. The Laplace operator on graphs; 1.1. The notion of a graph; 1.2. Cayley graphs; 1.3. Random walks; 1.4. The Laplace operator; 1.5. The Dirichlet problem; Chapter 2. Spectral properties of the Laplace operator; 2.1. Green's formula; 2.2. Eigenvalues of the Laplace operator; 2.3. Convergence to equilibrium; 2.4. More about the eigenvalues; 2.5. Convergence to equilibrium for bipartite graphs; 2.6. Eigenvalues of ℤ_{ }; 2.7. Products of graphs; 2.8. Eigenvalues and mixing time in ℤ_{ }ⁿ, odd.; 2.9. Eigenvalues and mixing time in a binary cube 5.3. Carne-Varopoulos estimate5.4. On-diagonal upper estimates of the heat kernel; 5.5. On-diagonal lower bound via the Dirichlet eigenvalues; 5.6. On-diagonal lower bound via volume growth; 5.7. Escape rate of random walk; Chapter 6. The type problem; 6.1. Recurrence and transience; 6.2. Recurrence and transience on Cayley graphs; 6.3. Volume tests for recurrence; 6.4. Isoperimetric tests for transience; Chapter 7. Exercises; Bibliography; Index; Back Cover
Series Title: University lecture series (Providence, R.I.), 71.
Responsibility: Alexander Grigor'yan.

Abstract:

Explores 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  Read more...

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