Prefer a chat interface with context about you and your work?
Asymptotic Behavior of the Dirichlet Energy on Poisson Point Clouds
We prove that quadratic pair interactions for functions defined on planar Poisson clouds and taking into account pairs of sites of distance up to a certain (large-enough) threshold can be almost surely approximated by the multiple of the Dirichlet energy by a deterministic constant. This is achieved by scaling the …