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Graphs and discrete Dirichlet spaces

Keller, Matthias.

Graphs and discrete Dirichlet spaces

Record Type:	Electronic resources : Monograph/item
Title/Author:	Graphs and discrete Dirichlet spacesby Matthias Keller, Daniel Lenz, Radoslaw K. Wojciechowski.
Author:	Keller, Matthias.
other author:	Lenz, Daniel.
Published:	Cham :Springer International Publishing :2021.
Description:	xv, 668 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Graph theory.
Online resource:	https://doi.org/10.1007/978-3-030-81459-5
ISBN:	9783030814595$q(electronic bk.)

Graphs and discrete Dirichlet spaces
Keller, Matthias.

Graphs and discrete Dirichlet spaces[electronic resource] /by Matthias Keller, Daniel Lenz, Radoslaw K. Wojciechowski. - Cham :Springer International Publishing :2021. - xv, 668 p. :ill., digital ;24 cm. - Grundlehren der mathematischen Wissenschaften,v. 3582196-9701 ;. - Grundlehren der mathematischen Wissenschaften ;348..

Part 0 Prelude -- Chapter 0 Finite Graphs -- Part 1 Foundations and Fundamental Topics -- Chapter 1 Infinite Graphs - Key Concepts -- Chapter 2 Infinite Graphs - Toolbox -- Chapter 3 Markov Uniqueness and Essential Self-Adjointness -- Chapter 4 Agmon-Allegretto-Piepenbrink and Persson Theorems -- Chapter 5 Large Time Behavior of the Heat Kernel -- Chapter 6 Recurrence -- Chapter 7 Stochastic Completeness -- Part 2 Classes of Graphs -- Chapter 8 Uniformly Positive Measure -- Chapter 9 Weak Spherical Symmetry -- Chapter 10 Sparseness and Isoperimetric Inequalities -- Part 3 Geometry and Intrinsic Metrics -- Chapter 11 Intrinsic Metrics: Definition and Basic Facts -- Chapter 12 Harmonic Functions and Caccioppoli Theory -- Chapter 13 Spectral Bounds -- Chapter 14 Volume Growth Criterion for Stochastic Completeness and Uniqueness Class -- Appendix A The Spectral Theorem -- Appendix B Closed Forms on Hilbert Spaces -- Appendix C Dirichlet Forms and Beurling-Deny Criteria -- Appendix D Semigroups, Resolvents and their Generators -- Appendix E Aspects of Operator Theory -- References -- Index -- Notation Index.

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.

ISBN: 9783030814595$q(electronic bk.)

Standard No.: 10.1007/978-3-030-81459-5doiSubjects--Topical Terms:

181880
Graph theory.

LC Class. No.: QA166 / .K45 2021

Dewey Class. No.: 511.5

Graphs and discrete Dirichlet spaces
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245 1 0 $a Graphs and discrete Dirichlet spaces $h [electronic resource] / $c by Matthias Keller, Daniel Lenz, Radoslaw K. Wojciechowski.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a xv, 668 p. : $b ill., digital ; $c 24 cm.
490 1 $a Grundlehren der mathematischen Wissenschaften, $x 2196-9701 ; $v v. 358
505 0 $a Part 0 Prelude -- Chapter 0 Finite Graphs -- Part 1 Foundations and Fundamental Topics -- Chapter 1 Infinite Graphs - Key Concepts -- Chapter 2 Infinite Graphs - Toolbox -- Chapter 3 Markov Uniqueness and Essential Self-Adjointness -- Chapter 4 Agmon-Allegretto-Piepenbrink and Persson Theorems -- Chapter 5 Large Time Behavior of the Heat Kernel -- Chapter 6 Recurrence -- Chapter 7 Stochastic Completeness -- Part 2 Classes of Graphs -- Chapter 8 Uniformly Positive Measure -- Chapter 9 Weak Spherical Symmetry -- Chapter 10 Sparseness and Isoperimetric Inequalities -- Part 3 Geometry and Intrinsic Metrics -- Chapter 11 Intrinsic Metrics: Definition and Basic Facts -- Chapter 12 Harmonic Functions and Caccioppoli Theory -- Chapter 13 Spectral Bounds -- Chapter 14 Volume Growth Criterion for Stochastic Completeness and Uniqueness Class -- Appendix A The Spectral Theorem -- Appendix B Closed Forms on Hilbert Spaces -- Appendix C Dirichlet Forms and Beurling-Deny Criteria -- Appendix D Semigroups, Resolvents and their Generators -- Appendix E Aspects of Operator Theory -- References -- Index -- Notation Index.
520 $a 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.
650 0 $a Graph theory. $3 181880
650 0 $a Dirichlet forms. $3 247428
650 1 4 $a Graph Theory. $3 522732
650 2 4 $a Functional Analysis. $3 274845
650 2 4 $a Probability Theory and Stochastic Processes. $3 274061
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 273786
650 2 4 $a Operator Theory. $3 274795
700 1 $a Lenz, Daniel. $3 515958
700 1 $a Wojciechowski, Radoslaw K. $3 908930
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Grundlehren der mathematischen Wissenschaften ; $v 348. $3 677391
856 4 0 $u https://doi.org/10.1007/978-3-030-81459-5
950 $a Mathematics and Statistics (SpringerNature-11649)