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<p>We prove optimal convergence rates for eigenvalues and eigenvectors of the graph Laplacian on Poisson point clouds. Our results are valid down to the critical percolation threshold, yielding error estimates for relatively sparse graphs.</p>

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Optimal Convergence Rates for the Spectrum of the Graph Laplacian on Poisson Point Clouds

  • 期刊论文

  • 发表日期：

    2025年1月22日

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  • Scott Armstrong,
  • Raghavendra Venkatraman

摘要

We prove optimal convergence rates for eigenvalues and eigenvectors of the graph Laplacian on Poisson point clouds. Our results are valid down to the critical percolation threshold, yielding error estimates for relatively sparse graphs.