Overview
- Presents a thorough study of geometric, analytic and probabilistic aspects of infinite graphs, including recent results
- Provides a very accessible introduction to general Dirichlet form theory by focusing on discrete spaces
- Relates spectral theory, the heat equation and intrinsic metrics on graphs
Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 358)
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Table of contents (15 chapters)
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Front Matter
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Prelude
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Front Matter
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Classes of Graphs
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Front Matter
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Geometry and Intrinsic Metrics
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Front Matter
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Keywords
About this book
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.
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Authors and Affiliations
About the authors
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.
Bibliographic Information
Book Title: Graphs and Discrete Dirichlet Spaces
Authors: Matthias Keller, Daniel Lenz, Radosław K. Wojciechowski
Series Title: Grundlehren der mathematischen Wissenschaften
DOI: https://doi.org/10.1007/978-3-030-81459-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-81458-8Published: 23 October 2021
eBook ISBN: 978-3-030-81459-5Published: 22 October 2021
Series ISSN: 0072-7830
Series E-ISSN: 2196-9701
Edition Number: 1
Number of Pages: XV, 668
Number of Illustrations: 4 b/w illustrations
Topics: Graph Theory, Functional Analysis, Probability Theory and Stochastic Processes, Global Analysis and Analysis on Manifolds, Operator Theory