Moyennes empiriques pour les mosaïques de Voronoi du disque de Poincaré

Let Φ be a stationary ergodic point process with finite intensity of the Poincaré disk. After defining the typical cell associated to the Voronoi tessellation of Φ, we study the convergence of empirical means of this tessellation. Contrary to the Euclidean case, several natural choices of means exist, leading to different behavior. The case where Φ is a Poisson process is more specifically characterized. To cite this article: F. Lips, C. R. Acad. Sci. Paris, Ser. I 342 (2006).