David Dereudre
Date et heure
Conférence - Géométrie Stochastique

The mini course is an introduction to the theory of Gibbs Point Processes (GPP). The GPP are models of interacting Point Processes which generalize the Poisson Point Processes for which the interaction is null. The interaction can be attractive, repulsive, depending of geometrical features...

In a first lecture, I will present several aspects of Finite volume GPP for which the definition is quite simple. These models are defined only on a bounded window in ${\Bbb R}^d$. However a lot of interesting questions are ever present in this setting: DLR equations, GNZ equations, variational principle, etc.

In a second lecture, I will introduce the more complicated formalism of Infinite volume GPP where the main issue is to define the GPP on the full space ${\Bbb R^d}$. We will see that the definition is implicit. The existence, uniqueness and non-uniqueness of GPP are non-trivial questions and we will discuss some of them.

In a last lecture, I will discuss the spatial statistic properties of GPP. The question is quite simple and natural. How to estimates the parameters of the model from the observations? Questions around asymptotic properties of the estimators appear naturally.