Journal of Applied Probability

A note on the simulation of the Ginibre point process

Laurent Decreusefond, Ian Flint, and Anais Vergne

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

J. Appl. Probab., Volume 52, Number 4 (2015), 1003-1012.

First available in Project Euclid: 22 December 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G55: Point processes 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60G60: Random fields
Secondary: 15A52

Determinantal point process Ginibre point process point process simulation


Decreusefond, Laurent; Flint, Ian; Vergne, Anais. A note on the simulation of the Ginibre point process. J. Appl. Probab. 52 (2015), no. 4, 1003--1012. doi:10.1239/jap/1450802749.

Export citation


  • Anderson, G. W., Guionnet, A. and Zeitouni, O. (2010). An Introduction to Random Matrices (Camb. Stud. Adv. Math. 118). Cambridge University Press.
  • Bornemann, F. (2011). On the scaling limits of determinantal point processes with kernels induced by Sturm-Liouville operators. Preprint. Available at
  • Decreusefond, L., Flint, I. and Vergne, A. (2013). Efficient simulation of the Ginibre point process. Preprint. Available at
  • Ginibre, J. (1965). Statistical ensembles of complex, quaternion, and real matrices. J. Math. Phys. 6, 440–449.
  • Heineman, E. R. (1929). Generalized Vandermonde determinants. Trans. Amer. Math. Soc. 31, 464–476.
  • Hough, J. B., Krishnapur, M., Peres, Y. and Virág, B. (2006). Determinantal processes and independence. Prob. Surv. 3, 206–229.
  • Hough, J. B., Krishnapur, M., Peres, Y. and Virág, B. (2009). Zeros of Gaussian Analytic Functions and Determinantal Point Processes (Univ. Lecture Ser. 51). American Mathematical Society, Providence, RI.
  • Lavancier, F., Møller, J. and Rubak, E. (2015). Determinantal point process models and statistical inference. J. R. Statist. Soc. B 77, 853–877.
  • Le Caër, G. and Delannay, R. (1993). The administrative divisions of mainland France as 2D random cellular structures. J. Phys. I 3, 1777–1800.
  • Le Caër, G. and Ho, J. S. (1990). The Voronoi tessellation generated from eigenvalues of complex random matrices. J. Phys. A 23, 3279.
  • Macchi, O. (1975). The coincidence approach to stochastic point processes. Adv. Appl. Prob. 7, 83–122.
  • Miyoshi, N. and Shirai, T. (2014). A cellular network model with Ginibre configurated base stations. Adv. Appl. Prob. 46, 832–845.
  • Scardicchio, A., Zachary, C. E. and Torquato, S. (2009). Statistical properties of determinantal point processes in high-dimensional Euclidean spaces. Phys. Rev. E (3) 79, 041108.
  • Shirai, T. (2006). Large deviations for the fermion point process associated with the exponential kernel. J. Statist. Phys. 123, 615–629.
  • Shirai, T. and Takahashi, Y. (2003). Random point fields associated with certain Fredholm determinants. I. Fermion, Poisson and boson point processes. J. Funct. Anal. 205, 414–463.
  • Soshnikov, A. (2000). Determinantal random point fields. Uspekhi Mat. Nauk 55, 107–160.
  • Tamura, H. and Ito, K. R. (2006). A canonical ensemble approach to the fermion/boson random point processes and its applications. Commun. Math. Phys. 263, 353–380.
  • Torrisi, G. L. and Leonardi, E. (2014). Large deviations of the interference in the Ginibre network model. Stoch. Syst. 4, 173–205.
  • Vergne, A., Flint, I., Decreusefond, L. and Martins, P. (2014). Disaster recovery in wireless networks: a homology-based algorithm. In ICT 2014 (Lisbon), pp. 226–230.