Our interest in this paper is to explore limit theorems for various geometric functionals of excursion sets of isotropic Gaussian random fields. In the past, limit theorems have been proven for various geometric functionals of excursion sets/sojourn times (see [4, 13, 14, 18, 22, 25] for a...

We investigate the asymptotics for two geometric measures, geometric quantiles and halfspace depths. While much literature is known on the population side, we fill out some gaps there to obtain a full picture, before turning to the sample versions, where the questions on asymptotics become...