Geometric probabilities involve the study of geometric figures, usually Euclidean, that have been randomly generated. This field of mathematics emerged in the 18th century and has enjoyed a recent boom, particularly in connection with the design and analysis of geometric algorithms.
In this talk, we provide a general introduction to some classical models and methods in geometric probability. In particular, we focus on the asymptotic study of convex random envelopes and certain properties of random mosaics, especially of the Poisson-Voronoi type.
