Graphs and Discrete Dirichlet Spaces von Matthias Keller | ISBN 9783030814595

Graphs and Discrete Dirichlet Spaces

von Matthias Keller, Daniel Lenz und Radosław K. Wojciechowski
Mitwirkende
Autor / AutorinMatthias Keller
Autor / AutorinDaniel Lenz
Autor / AutorinRadosław K. Wojciechowski
Buchcover Graphs and Discrete Dirichlet Spaces | Matthias Keller | EAN 9783030814595 | ISBN 3-030-81459-9 | ISBN 978-3-030-81459-5
“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)

Graphs and Discrete Dirichlet Spaces

von Matthias Keller, Daniel Lenz und Radosław K. Wojciechowski
Mitwirkende
Autor / AutorinMatthias Keller
Autor / AutorinDaniel Lenz
Autor / AutorinRadosław K. Wojciechowski

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.