Colloquium du CEREMADE

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Intervenant : DUVAL Céline (Sorbonne Université)
Titre :
Geometry of excursion sets: Computing the surface area from discretized points

Le : 05/11/2024 de : 15:30 à : 16:30
The excursion sets of a smooth random field carry information on the field that can be recovered using various geometric measures, such as the area or surface area of the excursion sets. After an introduction on these geometrical quantities, showing how they can be related to some parameters of the field, we focus on the problem of discretization. One never has access to the continuous observation of the excursion sets, but rather to observations at discrete points in space. In dimensions 2 and 3 and for specific regular grids, it has been reported that the usual estimate of the surface area of the excursion sets remains biased even when the grid becomes dense in the domain of observation. We study this limiting bias in any dimension and for polytopic tessellations. (Based on joint work with R. Cotsakis and E. Di Bernardino).
Salle : A709