Efficient simulation of the Ginibre point process

Laurent Decreusefond (1, 2) , Ian Flint (1, 2) , Anaïs Vergne (1, 2)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 Télécom ParisTech

The Ginibre point process is one of the main examples of deter- minantal point processes on the complex plane. It forms a recurring model in stochastic matrix theory as well as in pratical applications. However, this model has mostly been studied from a probabilistic point of view in the fields of stochastic matrices and determinantal point processes, and thus using the Ginibre process to model random phenomena is a topic which is for the most part unexplored. In order to obtain a determinantal point process more suited for simulation, we introduce a modified version of the classical kernel. Then, we compare three different methods to simulate the Ginibre point process and discuss the most efficient one depending on the application at hand.

Mots clés: Determinantal point process; Ginibre point process; simulation; simulation.

Domaines: Probabilités [math.PR]

Laurent Decreusefond, Ian Flint, Anaïs Vergne. Efficient simulation of the Ginibre point process. Journal of Applied Probability, 2015, 52 (4), pp.~. ⟨hal-00869259v2⟩