Eigenvalue gaps of the Laplacian of random graphs
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915199595839488 |
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| author | Christoffersen, Nicholas Luh, Kyle Nguyen, Hoi H. Wang, Jingheng |
| author_facet | Christoffersen, Nicholas Luh, Kyle Nguyen, Hoi H. Wang, Jingheng |
| contents | We show that, with very high probability, the random graph Laplacian has simple spectrum. Our method provides a quantitatively effective estimate of the spectral gaps. Along the way, we establish results on affine no-gaps delocalization, no-structure delocalization, overcrowding and small entries of the eigenvectors for the Laplacian model. These findings are of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00234 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Eigenvalue gaps of the Laplacian of random graphs Christoffersen, Nicholas Luh, Kyle Nguyen, Hoi H. Wang, Jingheng Probability Combinatorics We show that, with very high probability, the random graph Laplacian has simple spectrum. Our method provides a quantitatively effective estimate of the spectral gaps. Along the way, we establish results on affine no-gaps delocalization, no-structure delocalization, overcrowding and small entries of the eigenvectors for the Laplacian model. These findings are of independent interest. |
| title | Eigenvalue gaps of the Laplacian of random graphs |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2501.00234 |