Oriented distance point of view on random sets with application to shape optimization

Marc Dambrine (1) , Bénédicte Puig (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

Motivated by free boundary problems under uncertainties, we consider the oriented distance function as a way to define the expectation for a random compact or open set. In order to provide a large numbers law and a central limit theorem for this notion of expectation, we also adress the question of the convergence of the level sets of f n to the level sets of f when (f n) is a sequence of functions uniformly converging to f. We provide error estimates in terms of Hausdorff convergence. We illustrate our result on a free boundary problem.

Mots clés: Random sets; continuity of level sets; oriented distance functions; large numbers law; central limit theorem; free boundary problem

Domaines: Optimisation et contrôle [math.OC]

Marc Dambrine, Bénédicte Puig. Oriented distance point of view on random sets with application to shape optimization. 2019. ⟨hal-02057510v1⟩