Laplacians on Infinite Graphs
The main focus in this memoir is on Laplacians on both weighted graphs and weighted metric graphs. Let us emphasize that we consider infinite locally finite graphs and do not make any further geometric assumptions. Whereas the existing literature usually treats these two types of Laplacian operators...
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| Auteurs principaux: | , |
|---|---|
| Formato: | Livre numérique |
| Idioma: | Anglais |
| Publicado em: |
Berlin :
European Mathematical Society
2023.
Berlin : |
| Colecção: | Memoirs of the European Mathematical Society
3 |
| Acesso em linha: | Accès sur la plateforme EMS Press Accès sur la plateforme ISTEX Accès Université d'Orléans Accès INSA CVL |
| Nota: |
European Mathematical Society (Licence nationale) European Mathematical Society (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Laplacians on Infinite Graphs, 978-3-98547-025-9 |
| LEADER | 03192nam a22003977a 4500 | ||
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| 100 | 1 | |a Kostenko, Aleksey, |d 19..- | |
| 245 | 1 | 0 | |a Laplacians on Infinite Graphs |c Aleksey Kostenko, Noema Nicolussi. |
| 260 | |a Berlin : |b European Mathematical Society. | ||
| 260 | |a Berlin : |b European Mathematical Society, |c 2023. | ||
| 490 | 0 | |a Memoirs of the European Mathematical Society |x 2747-9099 |v 3 | |
| 500 | |a European Mathematical Society (Licence nationale) | ||
| 500 | |a European Mathematical Society (Licence nationale) | ||
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences | ||
| 506 | |a Accès libre en ligne à l'intégralité de la ressource | ||
| 520 | |a The main focus in this memoir is on Laplacians on both weighted graphs and weighted metric graphs. Let us emphasize that we consider infinite locally finite graphs and do not make any further geometric assumptions. Whereas the existing literature usually treats these two types of Laplacian operators separately, we approach them in a uniform manner in the present work and put particular emphasis on the relationship between them. One of our main conceptual messages is that these two settings should be regarded as complementary (rather than opposite) and exactly their interplay leads to important further insight on both sides. Our central goal is twofold. First of all, we explore the relationships between these two objects by comparing their basic spectral (self-adjointness, spectral gap, etc.), parabolic (Markovian uniqueness, recurrence, stochastic completeness, etc.), and metric (quasi isometries, intrinsic metrics, etc.) properties. In turn, we exploit these connections either to prove new results for Laplacians on metric graphs or to provide new proofs and perspective on the recent progress in weighted graph Laplacians. We also demonstrate our findings by considering several important classes of graphs (Cayley graphs, tessellations, and antitrees). | ||
| 700 | 1 | |a Nicolussi, Noema, |d 19..- |4 aut | |
| 776 | 0 | |t Laplacians on Infinite Graphs |z 978-3-98547-025-9 | |
| 856 | 4 | |u https://doi.org/10.4171/mems/3 |z Accès sur la plateforme EMS Press | |
| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-L50BFKQ9-5 |z Accès sur la plateforme ISTEX | |
| 856 | 4 | |5 452349901:833133594 |u https://ezproxy.univ-orleans.fr/login?url=https://doi.org/10.4171/mems/3 |z Accès Université d'Orléans | |
| 856 | 4 | |5 180339901:833136496 |u https://ezproxy.univ-orleans.fr/login?url=https://doi.org/10.4171/mems/3 |z Accès INSA CVL | |
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