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A note on the simulation of the Ginibre point process

Part of: Stochastic processes Special processes

Published online by Cambridge University Press:  30 March 2016

Laurent Decreusefond ,
Ian Flint  and
Anais Vergne
Laurent Decreusefond*
Affiliation:
Télécom Paristech
Ian Flint*
Affiliation:
Télécom Paristech
Anais Vergne*
Affiliation:
Télécom Paristech
*
∗Postal address: Télécom ParisTech, 46, rue Barrault, 75634 Paris cedex 13, France.
∗Postal address: Télécom ParisTech, 46, rue Barrault, 75634 Paris cedex 13, France.
∗Postal address: Télécom ParisTech, 46, rue Barrault, 75634 Paris cedex 13, France.
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Abstract

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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.

Keywords

Determinantal point processGinibre point processpoint process simulation

MSC classification

Primary: 60G55: Point processes 60K35: Interacting random processes; statistical mechanics type models; percolation theory 60G60: Random fields
Type
Research Papers
Information
Journal of Applied Probability , Volume 52 , Issue 4 , December 2015 , pp. 1003 - 1012
Copyright
Copyright © Applied Probability Trust 2015 

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