Close-up on random convex interfaces

In this talk, we investigate random convex interfaces which are generated as convex hulls of random point sets. We are interested in their asymptotic behavior when the size of the input goes to infinity. In a first part, we mainly identify average and maximal fluctuations in the radial and longitudinal directions through precise convergence results. We observe that the model shares some common features with the famous KPZ universality class of certain growth processes, including the scaling of type 1:2:3 or the appearance of a limit distribution similar to the Tracy-Widom distribution. In a second part, we consider the peeling procedure which consists in iterating the construction of the convex hull of the point set. The so-called layers are asymptotically governed by a deterministic analytical model and we study the geometric characteristics of each of the first layers. The talk is based on several joint works with Joe Yukich and Gauthier Quilan.