Séminaire MODAL'X : Bojan Basrak (University of Zagreb)

Résumé :  We consider stationary configurations of points in an Euclidean space which are marked by real-valued random variables we call scores. Such scores are allowed to depend on the relative positions of other points and outside sources of randomness. It turns out that in a neighbourhood of a point with an extreme score one can often rescale positions and scores of nearby points to obtain a limiting point process we refer to as the tail configuration. Under some assumptions on dependence between scores, based on this local limit one can derive global asymptotics for extreme scores in increasing sections of R^d. We apply this to study the (marked) Poisson processes where i) the scores depend on the distance to the k'th nearest neighbor and ii) where scores are allowed to propagate through a random network of points depending on their locations.