The Palm measure and the Voronoi tessellation for the Ginibre process

Details The Palm measure and the Voronoi tessellation for the Ginibre process The Palm measure and the Voronoi tessellation for the Ginibre process

2006-10-07

arxiv.org/abs/math/0610243v4

Annals of Applied Probability 2010, Vol. 20, No. 1, 90-128

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AAP620 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/09-AAP620

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.

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