Graphs and Discrete Dirichlet Spaces (Hardcover, 1st ed. 2021)

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 of the 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.

General

Imprint:	Springer Nature Switzerland AG
Country of origin:	Switzerland
Series:	Grundlehren der mathematischen Wissenschaften, 358
Release date:	October 2021
First published:	2021
Authors:	Matthias Keller • Daniel Lenz • Radoslaw K. Wojciechowski
Dimensions:	235 x 155mm (L x W)
Format:	Hardcover
Pages:	668
Edition:	1st ed. 2021
ISBN-13:	978-3-03-081458-8
Categories:	Books > Science & Mathematics > Mathematics > Numerical analysis Books > Science & Mathematics > Mathematics > Probability & statistics Books > Science & Mathematics > Mathematics > Combinatorics & graph theory Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
LSN:	3-03-081458-0
Barcode:	9783030814588

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