Gaussian Waves and Edge Eigenvectors of Random Regular Graphs
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912230904168448 |
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| author | He, Yukun Huang, Jiaoyang Yau, Horng-Tzer |
| author_facet | He, Yukun Huang, Jiaoyang Yau, Horng-Tzer |
| contents | Backhausz and Szegedy (2019) demonstrated that the almost eigenvectors of random regular graphs converge to Gaussian waves with variance $0\leq σ^2\leq 1$. In this paper, we present an alternative proof of this result for the edge eigenvectors of random regular graphs, establishing that the variance must be $σ^2=1$. Furthermore, we show that the eigenvalues and eigenvectors are asymptotically independent. Our approach introduces a simple framework linking the weak convergence of the imaginary part of the Green's function to the convergence of eigenvectors, which may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08897 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gaussian Waves and Edge Eigenvectors of Random Regular Graphs He, Yukun Huang, Jiaoyang Yau, Horng-Tzer Probability Mathematical Physics Combinatorics Spectral Theory 60B20, 05C80, 05C48, 60F05 Backhausz and Szegedy (2019) demonstrated that the almost eigenvectors of random regular graphs converge to Gaussian waves with variance $0\leq σ^2\leq 1$. In this paper, we present an alternative proof of this result for the edge eigenvectors of random regular graphs, establishing that the variance must be $σ^2=1$. Furthermore, we show that the eigenvalues and eigenvectors are asymptotically independent. Our approach introduces a simple framework linking the weak convergence of the imaginary part of the Green's function to the convergence of eigenvectors, which may be of independent interest. |
| title | Gaussian Waves and Edge Eigenvectors of Random Regular Graphs |
| topic | Probability Mathematical Physics Combinatorics Spectral Theory 60B20, 05C80, 05C48, 60F05 |
| url | https://arxiv.org/abs/2502.08897 |