Spectral convergence of graph Laplacians with Ricci curvature bounds and in non-collapsed Ricci limit spaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912441288359936 |
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| author | Inagaki, Masato |
| author_facet | Inagaki, Masato |
| contents | This paper establishes quantitative high-probability bounds on the eigenvalues and eigenfunctions of $ε$-neighborhood graph Laplacians constructed from i.i.d. random variables on $m$-dimensional closed Riemannian manifolds $(M,g)$ that satisfy a uniform lower Ricci curvature bound $\operatorname{Ric}_g\ge -(m-1)K$, a positive lower volume bound, and an upper diameter bound. These results extend to non-collapsed Ricci limit spaces that are measured Gromov-Hausdorff limits of such manifolds, and the bounds give a spectral approximation of weighted Laplacians on manifolds with non-smooth points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07427 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral convergence of graph Laplacians with Ricci curvature bounds and in non-collapsed Ricci limit spaces Inagaki, Masato Differential Geometry Metric Geometry Spectral Theory This paper establishes quantitative high-probability bounds on the eigenvalues and eigenfunctions of $ε$-neighborhood graph Laplacians constructed from i.i.d. random variables on $m$-dimensional closed Riemannian manifolds $(M,g)$ that satisfy a uniform lower Ricci curvature bound $\operatorname{Ric}_g\ge -(m-1)K$, a positive lower volume bound, and an upper diameter bound. These results extend to non-collapsed Ricci limit spaces that are measured Gromov-Hausdorff limits of such manifolds, and the bounds give a spectral approximation of weighted Laplacians on manifolds with non-smooth points. |
| title | Spectral convergence of graph Laplacians with Ricci curvature bounds and in non-collapsed Ricci limit spaces |
| topic | Differential Geometry Metric Geometry Spectral Theory |
| url | https://arxiv.org/abs/2506.07427 |