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New method expands spectral convergence analysis for graph Laplacians on manifolds

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Researchers have developed a method to derive first-order asymptotic expansions for the eigenvalues and eigenvectors of normalized graph Laplacians. These expansions are constructed from samples on Riemannian manifolds and include concentration inequalities for remainder terms, establishing weak convergence results. The analysis is notable for not requiring a multiplicity-one assumption on eigenvalues, broadening its applicability to manifolds with potentially repeated eigenvalue multiplicities. AI

RANK_REASON This is a research paper detailing a new mathematical method for analyzing graph Laplacians. [lever_c_demoted from research: ic=1 ai=0.4]

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

New method expands spectral convergence analysis for graph Laplacians on manifolds

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This is a research paper detailing a new mathematical method for analyzing graph Laplacians. [lever_c_demoted from research: ic=1 ai=0.4]
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COVERAGE [1]

  1. arXiv stat.ML TIER_1 English(EN) · Eunseong Bae, Wolfgang Polonik ·

    First-order asymptotic expansions for spectral convergence of normalized graph Laplacians constructed from samples on manifolds

    arXiv:2611.13623v1 Announce Type: cross Abstract: Under i.i.d. uniform sampling from a closed Riemannian manifold embedded in Euclidean space, we derive first-order asymptotic expansions for the eigenvalues and eigenvectors of symmetrically normalized graph Laplacians constructed…

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