Spatial point patterns emerge in many applications: in forestry (e.g. locations of plants/trees), environmental sciences (e.g. lightning strike impacts in France), economis (locations of banks), astrophysics (e.g. sunspots),... Even in the stationary case, many models exist in the literature to model clustering effects or repulsion between points/objects, such as Cox, Gibbs or determinantal point processes to cite a few. I will present a "new" class of stochastic models, simply obtained as critical points obtained from a Gaussian random field. The topic of zeroes or critical points of (Gaussian) random fields has given rise to a huge literature, ... and I would say essentially, in the probability community. This is why by "new", I mean that I'll be focusing on properties and problems of these models useful for statistical applications. These points deal with understanding precisely first and second moments, problems related to the simulation of such models and asymptotic results for functionals of these point processes.
[Joint work with Julien Chevallier (LJK) and Rasmus Waagepetersen (Aalborg University, Denmark)]