Date/heure
12 octobre 2023
10:45 - 11:45
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Tara Trauthwein (Université du Luxembourg)
Catégorie d'évènement Séminaire Probabilités et Statistique
Résumé
Imagine a collection of randomly distributed points in space, and build a graph on it according to some rules. We now take the sum of all edge lengths and want to know if this sum verifies a central limit theorem. In our context, the random collection of points is given by a Poisson measure and the sum of edge lengths is an example of a Poisson functional. In this talk, using the so-called Malliavin-Stein method, we show a result which allows us to derive central limit theorems, as well as speeds of convergence, for functionals of general Poisson measures, under minimal moment assumptions. Our main application is the closure of a conjecture about a convergence result of the Online Nearest Neighbour Graph.