, Professeur, Laboratoire Paul Painlevé, Université de Lille - Sciences et Technologies
In this talk, we will discuss several questions around the connectivity of random geometrical graphs based on an infinite number of vertices uniformly distributed in the plane. We will focus on the percolation property which mainly refer to the existence of an infinite connected component in the graph structure. We will present phase transition phenomenons for which the percolation occurs if and only if a parameter is large enough. This theory have many applications in material science, telecommunication, and statistical physics when scientists try to explain for instance the permeability or conductivity of materials, the range of communication between sensors, the phase transition between solid, liquid and gaz in the water.