Graphs and Discrete Dirichlet Spaces

Daniel Lenz, Matthias Keller, Radoslaw K. Wojciechowski

ISBN 10: 3030814580 / ISBN 13: 9783030814588

Editore: Springer Nature Switzerland AG, CH, 2021

Codice articolo LU-9783030814588

Riassunto:

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.

Informazioni sull?autore: Matthias Keller studied in Chemnitz and obtained his PhD in Jena. He held positions in Princeton, Jerusalem and Haifa before becoming a professor at the University of Potsdam.

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.

Dati bibliografici

Titolo: Graphs and Discrete Dirichlet Spaces
Casa editrice: Springer Nature Switzerland AG, CH
Data di pubblicazione: 2021
Legatura: Hardback
Condizione: New
Edizione: 1st ed. 2021.