Date/heure
21 novembre 2025
11:00 - 12:00
Oratrice ou orateur
Matteo d'Achille (IECL)
Catégorie d'évènement Séminaire EDP, Analyse et Applications (Metz)
Résumé
A Euclidean Random Assignment Problem (ERAP) is the study of the random optimal cost of assigning blue points to red points, where these two sets form independent binomial point processes on the same metric space.
Originally introduced in physics more than three decades ago as toy models for spin glasses, ERAPs serve as discrete analogues of the celebrated Monge–Kantorovich problem in optimal transport and have found numerous applications, including in satellite-based Earth observation.
In this talk, I will first introduce ERAPs and review known results for cases where the underlying metric space has additional structure, such as Euclidean spaces of dimension $d \geq 1$.
Then I will show that, when blue and red points are uniformly distributed on the unit circle, the cost of the quadratic ERAP is asymptotically distributed as $\sum_{k=1}^\infty E_k$, where $(E_k)_{k \geq 1}$ is a family of independent $\mathrm{Exp}(k^2)$ random variables.
Talk mostly based on my PhD Thesis.