# Mean asymptotics for a Poisson-Voronoi cell on a Riemannian manifold

@article{Calka2018MeanAF, title={Mean asymptotics for a Poisson-Voronoi cell on a Riemannian manifold}, author={Pierre Calka and Aur'elie Chapron and Nathanael Enriquez}, journal={arXiv: Probability}, year={2018} }

In this paper, we consider a Riemannian manifold $M$ and the Poisson-Voronoi tessellation generated by the union of a fixed point $x_0$ and a Poisson point process of intensity $\lambda$ on $M$. We obtain asymptotic expansions up to the second order for the means of several characteristics of the Voronoi cell associated with $x_0$, including its volume and number of vertices. In each case, the first term of the estimate is equal to the mean characteristic in the Euclidean setting while the…

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