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

Scott Armstrong; Raghavendra Venkatraman

doi:10.1007/s10208-025-09696-9

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

Scott Armstrong, Raghavendra Venkatraman

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Journal	Foundations of Computational Mathematics
DOIs	https://doi.org/10.1007/s10208-025-09696-9
State	Accepted/In press - 2025

Keywords

Convergence rates for spectrum
Graph laplacian
Stochastic homogenization

ASJC Scopus subject areas

Analysis
Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

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10.1007/s10208-025-09696-9

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title = "Optimal Convergence Rates for the Spectrum of the Graph Laplacian on Poisson Point Clouds",

abstract = "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.",

keywords = "Convergence rates for spectrum, Graph laplacian, Stochastic homogenization",

author = "Scott Armstrong and Raghavendra Venkatraman",

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language = "English (US)",

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AU - Venkatraman, Raghavendra

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PY - 2025

Y1 - 2025

N2 - 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.

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KW - Convergence rates for spectrum

KW - Graph laplacian

KW - Stochastic homogenization

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

Abstract

Keywords

ASJC Scopus subject areas

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