Delocalized eigenvectors of transitive graphs and beyond
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917009621516288 |
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| author | Burq, Nicolas Letrouit, Cyril |
| author_facet | Burq, Nicolas Letrouit, Cyril |
| contents | We prove delocalization of eigenvectors of vertex-transitive graphs via elementary estimates of the spectral projector. We recover in this way known results which were formerly proved using representation theory. Similar techniques show that for general symmetric matrices, most approximate eigenvectors spectrally localized in a given window containing sufficiently many eigenvalues are delocalized in $L^q$ norms. Building upon this observation, we prove a delocalization result for approximate eigenvectors of large graphs containing few short loops, under an assumption on the resolvent which is verified in some standard cases, for instance random lifts of a fixed base graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12384 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Delocalized eigenvectors of transitive graphs and beyond Burq, Nicolas Letrouit, Cyril Spectral Theory We prove delocalization of eigenvectors of vertex-transitive graphs via elementary estimates of the spectral projector. We recover in this way known results which were formerly proved using representation theory. Similar techniques show that for general symmetric matrices, most approximate eigenvectors spectrally localized in a given window containing sufficiently many eigenvalues are delocalized in $L^q$ norms. Building upon this observation, we prove a delocalization result for approximate eigenvectors of large graphs containing few short loops, under an assumption on the resolvent which is verified in some standard cases, for instance random lifts of a fixed base graph. |
| title | Delocalized eigenvectors of transitive graphs and beyond |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2407.12384 |