Connectivity of nodes

Contents Introduction Theory for the Poisson 1d model Order statistics theory Exact theory for the fixed-n 1d model Probability of connectivity for the fixed-n 1d model Simulation results-fixed-n 1d model Theory for the Poisson 2d model Simulation results-fixed-n 2d model Unit square Unit torus Unit-radius disk Distance distribution for some regions Triangles Asymptotics for near neighbours Exact theory for mean distances on a torus Almost sure connectivity results References Connectivity of nodes 2 of 44