On the exact distribution of the Isotropic Planar Point Processes of Phase type

The Isotropic Phase Planar Point Process differs from the Poisson process on the plane by introducing clusters effects and dependence between sets of points. We propose to develop several analytical expressions of the moments and the exact distribution of the numbers of points in any polar rectangle of the plane by highlighting the similarities in those egalities. This work is the first step towards a complete determination of the finite dimensional distribution of the process, and is motivated by a performance study in wireless telecommunication. Our objective here is to illustrate the diverse techniques which may be used in such spatial problems. We also discuss the numerical efficiency when solving those problems.