A note on the simulation of the Ginibre point process. (December 2015)

• Record Type: Journal Article
• Authors: Decreusefond, Laurent; Flint, Ian; Vergne, Anais
• Is Part Of: Journal of applied probability. Volume 52:Number 4(2015)
• Page Start: 1003
• Page End: 1012
• Publication Date: 2015-12
• Subjects: Determinantal point process, -- Ginibre point process, -- point process simulation; 60G55, -- 60K35, -- 60G60, -- 15A52; 519.2
• DOI: 10.1239/jap/1450802749
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract : The Ginibre point process (GPP) is one of the main examples of determinantal point processes on the complex plane. It is a recurring distribution of random matrix theory as well as a useful model in applied mathematics. In this paper we briefly overview the usual methods for the simulation of the GPP. Then we introduce a modified version of the GPP which constitutes a determinantal point process more suited for certain applications, and we detail its simulation. This modified GPP has the property of having a fixed number of points and having its support on a compact subset of the plane. See Decreusefond et al. (2013) for an extended version of this paper.