The Annals of Applied Probability

The Palm measure and the Voronoi tessellation for the Ginibre process

André Goldman

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Abstract

We prove that the Palm measure of the Ginibre process is obtained by removing a Gaussian distributed point from the process and adding the origin. We obtain also precise formulas describing the law of the typical cell of Ginibre–Voronoi tessellation. We show that near the germs of the cells a more important part of the area is captured in the Ginibre–Voronoi tessellation than in the Poisson–Voronoi tessellation. Moment areas of corresponding subdomains of the cells are explicitly evaluated.

Article information

Source
Ann. Appl. Probab., Volume 20, Number 1 (2010), 90-128.

Dates
First available in Project Euclid: 8 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1262962319

Digital Object Identifier
doi:10.1214/09-AAP620

Mathematical Reviews number (MathSciNet)
MR2582643

Zentralblatt MATH identifier
1197.60047

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 60G55: Point processes 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Ginibre process Palm measure determinantal process stochastic domination Voronoi tessellation

Citation

Goldman, André. The Palm measure and the Voronoi tessellation for the Ginibre process. Ann. Appl. Probab. 20 (2010), no. 1, 90--128. doi:10.1214/09-AAP620. https://projecteuclid.org/euclid.aoap/1262962319


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