Limit Theorems for the Generalized Perimeters of Random Inscribed Polygons: II

Recently, W. Lao and M. Mayer (2008) developed U-max-statistics, where instead of averaging the values of the kernel over various subsets, the maximum of the kernel is considered. Such statistics often appear in stochastic geometry. This is the second part of the work devoted to the study of the generalized perimeter of a random inscribed polygon and the limit behavior of U-max-statistics related to it. Here we consider the case where the parameter arising in the definition of a generalized perimeter exceeds 1. The limit theorems in the case of a triangle are formulated and proved.