A note on the simulation of the Ginibre point process

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.

[1]  Y. Peres,et al.  Determinantal Processes and Independence , 2005, math/0503110.

[2]  J. Møller,et al.  Determinantal point process models and statistical inference , 2012, 1205.4818.

[3]  Philippe Martins,et al.  Disaster recovery in wireless networks: A homology-based algorithm , 2014, 2014 21st International Conference on Telecommunications (ICT).

[4]  Александр Борисович Сошников,et al.  Детерминантные случайные точечные поля@@@Determinantal random point fields , 2000 .

[5]  T. Shirai,et al.  Random point fields associated with certain Fredholm determinants I: fermion, Poisson and boson point processes , 2003 .

[6]  G. Le Caër,et al.  The Voronoi tessellation generated from eigenvalues of complex random matrices , 1990 .

[7]  N. Miyoshi,et al.  A cellular network model with Ginibre configurated base stations , 2012 .

[8]  Emilio Leonardi,et al.  Large deviations of the interference in the Ginibre network model , 2013, ArXiv.

[9]  J. Ginibre.  Statistical Ensembles of Complex, Quaternion, and Real Matrices , 1965 .

[10]  H. Tamura,et al.  A Canonical Ensemble Approach to the Fermion/Boson Random Point Processes and Its Applications , 2005, math-ph/0501053.

[11]  O. Macchi.  The coincidence approach to stochastic point processes , 1975, Advances in Applied Probability.

[12]  Yuval Peres,et al.  Zeros of Gaussian Analytic Functions and Determinantal Point Processes , 2009, University Lecture Series.

[13]  Tomoyuki Shirai,et al.  Large Deviations for the Fermion Point Process Associated with the Exponential Kernel , 2006 .

[14]  E. Heineman.  Generalized Vandermonde determinants , 1929 .

[15]  Chase E. Zachary,et al.  Statistical properties of determinantal point processes in high-dimensional Euclidean spaces. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Renaud Delannay,et al.  The administrative divisions of mainland France as 2D random cellular structures , 1993 .