Graphs and Discrete Dirichlet Spaces

Graphs and Discrete Dirichlet Spaces

AngličtinaEbook
Keller, Matthias
Springer International Publishing
EAN: 9783030814595
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Podrobné informace

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.
EAN 9783030814595
ISBN 3030814599
Typ produktu Ebook
Vydavatel Springer International Publishing
Datum vydání 22. října 2021
Jazyk English
Autoři Keller, Matthias; Lenz, Daniel; Wojciechowski, Radoslaw K.
Série Grundlehren der mathematischen Wissenschaften