Essential spectrum and Weyl asymptotics for discrete Laplacians
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BONNEFONT, Michel | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | GOLENIA, Sylvain | |
| dc.date.accessioned | 2024-04-04T03:22:34Z | |
| dc.date.available | 2024-04-04T03:22:34Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194769 | |
| dc.description.abstractEn | In this paper, we investigate spectral properties of discrete Laplacians. Our study is based on the Hardy inequality and the use of super-harmonic functions. We recover and improve lower bounds for the bottom of the spectrum and of the essential spectrum. In some situation, we obtain Weyl asymptotics for the eigenvalues. We also provide a probabilistic representation of super-harmonic functions. Using coupling arguments, we set comparison results for the bottom of the spectrum, the bottom of the essential spectrum and the stochastic completeness of different discrete Laplacians. The class of weakly spherically symmetric graphs is also studied in full detail. | |
| dc.language.iso | en | |
| dc.subject.en | discrete Laplacian | |
| dc.subject.en | locally finite graphs | |
| dc.subject.en | asympotic of eigenvalues | |
| dc.subject.en | spectrum | |
| dc.subject.en | essential spectrum | |
| dc.subject.en | markov chains | |
| dc.subject.en | functional inequalities | |
| dc.title.en | Essential spectrum and Weyl asymptotics for discrete Laplacians | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Théorie spectrale [math.SP] | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.identifier.arxiv | 1406.5391 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-01010730 | |
| hal.version | 1 | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01010730v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BONNEFONT,%20Michel&GOLENIA,%20Sylvain&rft.genre=preprint |
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