Spectral convergence of graph Laplacians with Ricci curvature bounds and in non-collapsed Ricci limit spaces

Masato Inagaki

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arXiv · 2506.07427

Spectral convergence of graph Laplacians with Ricci curvature bounds and in non-collapsed Ricci limit spaces

Masato Inagaki

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Abstract

This paper establishes quantitative high-probability bounds on the eigenvalues and eigenfunctions of $\epsilon$-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.

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Masato Inagaki. 2025-06-09. Spectral convergence of graph Laplacians with Ricci curvature bounds and in non-collapsed Ricci limit spaces. https://arxiv.org/abs/2506.07427

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