Date/heure
1 décembre 2025
14:00 - 16:00
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Matteo D'Achille
Catégorie d'évènement Géométrie
Résumé
IPVTs and applications
I will discuss limits in low intensity of Poisson-Voronoi tessellations, which we called ideal Poisson-Voronoi tessellations (IPVTs).
In the colloquium part, I will focus on the IPVT of real hyperbolic space of dimension d, where a simple Poissonian description of the cell containing the origin enables an in-depth study of the geometric features of its tiles.
In the research seminar part, I will discuss sufficient conditions for convergence toward IPVTs in a general metric space, and illustrate them for the Cartesian product of two hyperbolic planes endowed with the $L^1$ metric. Then I will discuss an application to proving the smallness of the uniqueness threshold of Poisson/Bernoulli–Voronoi percolation on spaces with a non-amenable product structure.
Based on joint works with Nicolas Curien, Nathanaël Enriquez, Russell Lyons, Meltem Ünel (2303.16831, to appear on The Annals of Probability), on 2412.00822, and on incoming works with Ali Khezeli and with Jan Grebik, Ali Khezeli, Konstantin Recke, and Amanda Wilkens.