Poisson convergence in two dimensions with application to row and column exchangeable arrays (Q1819818)

The behaviour of a simple point process on the plane can be described by studying two associated compensators (dual predictable projections). The main result of the paper using this principle is a Poisson convergence theorem for a sequence of simple point processes in the plane. Sufficient conditions for the convergence to a Poisson process are given in terms of the behaviour of the two sequences of compensators. One application is a functional Poisson convergence result for a sequence of row and column exchangeable arrays.