A generalisation of the fractional Brownian field based on non-Euclidean norms

We explore a generalisation of the L´evy fractional Brownian field on the Euclidean space based on replacing the Euclidean norm with another norm. A characterisation result for admissible norms yields a complete description of all self-similar Gaussian random fields with stationary increments. Several integral representations of the introduced random fields are derived. In a similar vein, several non-Euclidean variants of the fractional Poisson field are introduced and it is shown that they share the covariance structure with the fractional Brownian field and converge to it. The shape parameters of the Poisson and Brownian variants are related by convex geometry transforms, namely the radial pth mean body and the polar projection transforms.

European Public Sphere

Political communication scholars have investigated whether a public sphere emerges that adapts to the new supra- and intergovernmental European reality in the course of European Union integration. Such European public sphere(s) might link EU politics to citizens. The entry discusses not only how such Europeanized public sphere might affect the quality of democracy as well as the political process but also what a European public sphere could look like and how we might measure it. Our empirical knowledge on the existence or nonexistence of a European Public Sphere is summarized in five theses. The article concludes with future paths for research.