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.

翻译：我们证明泊松点云上图拉普拉斯算子的特征值与特征向量的最优收敛速度。结果在临界渗流阈值以下仍成立，从而为相对稀疏的图提供了误差估计。