Date/heure
9 janvier 2025
10:45 - 11:45
Lieu
Salle de conférences Nancy
Oratrice ou orateur
David Dereudre (Université de Lille)
Catégorie d'évènement Séminaire Probabilités et Statistique
Résumé
In this talk, we discuss the question of Gibbs point processes in R^d with pairwise interactions that are not integrable at infinity. A standard example is the Riesz potential of the form g(x)=1/|x|^s where s<d. This setting has a long history, notably because the case s=d-2 corresponds to the classical Coulomb potential, which arises from electrostatic theory. We will first address the existence of the process in the infinite volume regime when a neutralizing background is introduced (this model is known as Jellium in theoretical physics). Subsequently, we will discuss the rigidity of such point processes, specifically hyper-uniformity and number rigidity. We will provide a state-of-the-art review and present numerous conjectures and open problems.