Geometry and spectrum of rapidly branching graphs
- We study graphs whose vertex degree tends to infinity and which are, therefore, called rapidly branching. We prove spectral estimates, discreteness of spectrum, first order eigenvalue and Weyl asymptotics solely in terms of the vertex degree growth. The underlying techniques are estimates on the isoperimetric constant. Furthermore, we give lower volume growth bounds and we provide a new criterion for stochastic incompleteness. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
| Author details: | Matthias Keller, Florentin MünchGND, Felix PogorzelskiORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1002/mana.201400349 |
| ISSN: | 0025-584X |
| ISSN: | 1522-2616 |
| Title of parent work (English): | Mathematische Nachrichten |
| Publisher: | Wiley-VCH |
| Place of publishing: | Weinheim |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2016 |
| Publication year: | 2016 |
| Release date: | 2020/03/22 |
| Tag: | Graph Laplacians; discrete spectrum; eigenvalue asymptotics; isoperimetric estimates; stochastic completeness |
| Volume: | 289 |
| Number of pages: | 12 |
| First page: | 1636 |
| Last Page: | 1647 |
| Funding institution: | German Research Foundation (DFG) |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| Peer review: | Referiert |
