A NOTE ON THE SIMULATION OF THE GINIBRE POINT PROCESS

被引：27

作者：

Decreusefond, Laurent ^{[1
]}

Flint, Ian ^{[1
]}

Vergne, Anais ^{[1
]}

机构：

[1] Telecom ParisTech, 46 Rue Barrault, F-75634 Paris 13, France

来源：

JOURNAL OF APPLIED PROBABILITY | 2015年 / 52卷 / 04期

关键词：

Determinantal point process; Ginibre point process; point process simulation; FERMION;

D O I：

10.1017/S002190020011304X

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：1003 / 1012

页数：10

共 19 条

[1]

Anderson G. W., 2010, CAMB STUD ADV MATH, V118

[2] Determinantal Processes and Independence [J].

Ben Hough, J. ;

Krishnapur, Manjunath ;

Peres, Yuval ;

Virag, Balint .

PROBABILITY SURVEYS, 2006, 3 :206-229

[3]

Bornemann F., 2011, PREPRINT

[4]

Decreusefond L., 2013, PREPRINT

[5] STATISTICAL ENSEMBLES OF COMPLEX QUATERNION AND REAL MATRICES [J].

GINIBRE, J .

JOURNAL OF MATHEMATICAL PHYSICS, 1965, 6 (03) :440-&

[6] Generalized Vandermonde determinants [J].

Heineman, E. R. .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1929, 31 (1-4) :464-476

[7]

Hough J.B., 2009, U LECT SER, V51

[8] Determinantal point process models and statistical inference [J].

Lavancier, Frederic ;

Moller, Jesper ;

Rubak, Ege .

JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 2015, 77 (04) :853-877

[9]

LECAER G, 1990, J PHYS A-MATH GEN, V23, P3279, DOI 10.1088/0305-4470/23/14/025

[10] THE ADMINISTRATIVE DIVISIONS OF MAINLAND FRANCE AS 2D RANDOM CELLULAR STRUCTURES [J].

LECAER, G ;

DELANNAY, R .

JOURNAL DE PHYSIQUE I, 1993, 3 (08) :1777-1800

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