Speaker
Description
In this talk we introduce the Poisson-Voronoi tessellation, a classical model of random mosaic based on seeds placed randomly in the plane, each associated with a Voronoi cell, consisting of all points of the plane closer to that seed than to any other. These cells can be seen as influence zones of the seeds.
The statistical properties of these mosaics (average area, average number of vertices, extreme values, etc.) have been extensively studied since the 20th century, first in the plane and then in $R^n$, some examples of which we present.
We then extend the model to a non-Euclidean framework, specifically on Riemannian surfaces, with a twofold aim : investigate properties of the tessellation and relate this to the geometrical characteristics of the surface, namely the Gaussian curvature.