Showing 2023Show all
3 papers · 1 filter
math.AP2023
Optimal convergence rates for the spectrum of the graph Laplacian on Poisson point clouds
Scott Armstrong, Raghavendra Venkatraman
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…
math.AP2023
Dirichlet eigenfunctions with nonzero mean value
Stefan Steinerberger, Raghavendra Venkatraman
We consider Laplacian eigenfunctions on a domain . Under Neumann boundary conditions, the first eigenfunction is constant and the others have mean value 0. T…
math.PR2023
Quantitative homogenization and large-scale regularity of Poisson point clouds
Scott Armstrong, Raghavendra Venkatraman
We prove quantitative homogenization results for harmonic functions on supercritical continuum percolation clusters--that is, Poisson point clouds with edges connecting points whic…