Resumen de Deterministic thinning of finite Poisson processes

Omer Angel, Alexander E. Holroyd, Terry Soo

• Let and be homogeneous Poisson point processes on a fixed set of finite volume. We prove a necessary and sufficient condition on the two intensities for the existence of a coupling of and such that is a deterministic function of , and all points of are points of . The condition exhibits a surprising lack of monotonicity. However, in the limit of large intensities, the coupling exists if and only if the expected number of points is at least one greater in than in .