Aurélien Vasseur | Searcharxiv

arXiv2018

Stein's method and Papangelou intensity for Poisson or Cox process approximation

In this paper, we apply the Stein's method in the context of point processes, namely when the target measure is the distribution of a finite Poisson point process. We show that the so-called Kantorovich-Rubinstein distance between such a measure and another finite point process is bounded by the $L^1$-distance between their respective Papangelou intensities. Then, we deduce some convergence rates for sequences of point processes approaching a Poisson or a Cox point process.

math.PR↗

arXiv2015

A case study on regularity in cellular network deployment

This paper aims to validate the $β$-Ginibre point process as a model for the distribution of base station locations in a cellular network. The $β$-Ginibre is a repulsive point process in which repulsion is controlled by the $β$ parameter. When $β$ tends to zero, the point process converges in law towards a Poisson point process. If $β$ equals to one it becomes a Ginibre point process. Simulations on real data collected in Paris (France) show that base station locations can be fitted with a $β$-Ginibre point process. Moreover we prove that their superposition tends to a Poisson point process as it can be seen from real data. Qualitative interpretations on deployment strategies are derived from the model fitting of the raw data.

math.PR↗