Díaz Báñez, José MiguelGarijo Royo, DeliaMárquez Pérez, AlbertoUrrutia Galicia, Jorge2017-05-222017-05-222013Balogh, J., González Aguilar, H. y Salazar Anaya, G. (2013). Empty convex polytopes in random point sets. En XV Spanish Meeting on Computational Geometry, Sevilla.http://hdl.handle.net/11441/60155Given a set P of points in Rd, a convex hole (alternatively, empty convex polytope) of P is a convex polytope with vertices in P, containing no points of P in its interior. Let R be a bounded convex region in Rd. We show that if P is a set of n random points chosen independently and uniformly over R, then the expected number of vertices of the largest hole of P is Θ(log n/(log log n)), regardless of the shape of R. This generalizes the analogous result proved for the case d = 2 by Balogh, González-Aguilar, and Salazar.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/openAccess