The Palm measure and the Voronoi tessellation for the Ginibre process

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.