Asymptotic poisson distribution in isotropic ph planar point processes

We consider a family of planar point processes which are a natural generalization of the two-dimensional Poisson process. In this family, points are located on a sequence of concentric circles centered at the origin; the radii of the circles are chosen through a phase-type construction, the points on each circle are uniformly distributed. These processes are called isotropic PH planar point processes for short. Although point patterns obtained in this fashion are very different from those of the Poisson process, nevertheless we show that if one considers the region of the plane far away from the origin, the PH processes exhibit some similarities to the Poisson process.