Konwersatorium im. Leopolda Infelda

Let there be given a random set of point-like "particles" in the plane. The Voronoi construction assigns to each particle a cell in such a way that every generic point of the plane is in the cell of the particle to which it is closest. Voronoi cells are convex polygons that meet at trivalent vertices. They may, among many other things, model nat- urally occurring cellular structures. Their statistics has given rise to research by mathematicians, physicists and other scientists. Our inves- tigation starts from the following question: what is the probability that a randomly picked Voronoi cell have n sides, in particular when n is a large number? We will describe new exact results, a new simulation method, and an application in an experimental context.