Limiting point processes in the branching random walk

Abstract

Take the nth generation of a supercritical branching random walk (a spatially homogeneous branching process) as a process of cluster centres and take independent copies of some simple point process Y as the clusters. Let the resulting point process be Yn. For a given sequence of real numbers {xn} let Yn be centred on xn. Under certain conditions, when an appropriate scale change is made, the resulting point process converges in distribution to a non-trivial limit.