Overview
The spectral geometry of infinite graphs deals with three major themes and their interplay: the spectral theory of the Laplacian, the geometry of the underlying graph, and the heat flow with its probabilistic aspects. In this book, all three themes are brought together coherently under the perspective of Dirichlet forms, providing a powerful and unified approach. The book gives a complete account of key topics of infinite graphs, such as essential self-adjointness, Markov uniqueness, spectral estimates, recurrence, and stochastic completeness. A major feature of the book is the use of intrinsic metrics to capture the geometry of graphs. As for manifolds, Dirichlet forms in the graph setting offer a structural understanding of the interaction between spectral theory, geometry and probability. For graphs, however, the presentation is much more accessible and inviting thanks to the discreteness of the underlying space, laying bare the main concepts while preserving the deep insights ofthe manifold case. Graphs and Discrete Dirichlet Spaces offers a comprehensive treatment of the spectral geometry of graphs, from the very basics to deep and thorough explorations of advanced topics. With modest prerequisites, the book can serve as a basis for a number of topics courses, starting at the undergraduate level.
Full Product Details
Author: Matthias Keller ,
Daniel Lenz ,
Radosław K. Wojciechowski
Publisher: Springer Nature Switzerland AG
Imprint: Springer Nature Switzerland AG
Edition: 1st ed. 2021
Volume: 358
Weight: 1.184kg
ISBN: 9783030814588
ISBN 10: 3030814580
Pages: 668
Publication Date: 23 October 2021
Audience:
Professional and scholarly
,
College/higher education
,
Professional & Vocational
,
Postgraduate, Research & Scholarly
Format: Hardback
Publisher's Status: Active
Availability: Manufactured on demand
We will order this item for you from a manufactured on demand supplier.
Reviews
This is an extremely well-written book, with motivations sprinkled throughout. One useful pedagogic device is the slow beginning with a chapter 0 giving the finite case separately, even though this is technically superfluous. The value of the book is enhanced by its many exercises. Undergraduate students and researchers should find it an extremely useful introduction to a beautiful theory. (Bhaskar Bagchi, zbMATH 1487.05003, 2022)
“This is an extremely well-written book, with motivations sprinkled throughout. One useful pedagogic device is the slow beginning with a chapter 0 giving the finite case separately, even though this is technically superfluous. The value of the book is enhanced by its many exercises. Undergraduate students and researchers should find it an extremely useful introduction to a beautiful theory.” (Bhaskar Bagchi, zbMATH 1487.05003, 2022)
Author Information
Matthias Keller studied in Chemnitz and obtained his PhD in Jena. He held positions in Princeton, Jerusalem and Haifa before becoming a professor at the University of Potsdam. Daniel Lenz obtained his PhD in Frankfurt am Main. After prolonged stays in Jerusalem, Chemnitz and Houston, he is now a professor at the Friedrich Schiller University in Jena. Radoslaw Wojciechowski got his PhD at the Graduate Center of the City University of New York following his undergraduate studies at Indiana University Bloomington. After a postdoc period in Lisbon he is now a professor at York College and the Graduate Center in New York City.
