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...

We consider the correlation structure of the random coefficients for a class of wavelet systems on the sphere (labelled Mexican needlets) which was recently introduced in the literature by [D. Geller, A. Mayeli, Nearly tight frames and space-frequency analysis on compact manifolds, Preprint,...

Strategic complementarities can lead to multiple Nash equilibria in macro-economic models. When this is the case of a decentralized economy, agents have to choose their strategy on the basis of the expected behaviour of other agents, but the concept of rational expectations is not a guide to...

In this paper we provide some simple characterizations for the spherical harmonics coefficients of an isotropic random field on the sphere. The main result is a characterization of isotropic gaussian fields through independence of the coefficients of their development in spherical harmonics.