Conference Agenda

Non-stationary random fields under the physical dependence measure are investigated. In particular, the objective is to study the maximum of local averages given an increasing bandwidth under expanding-domain asymptotics. By defining suitable vectors based on the studied random field it becomes possible to use the concept of dependency graphs known from time series analysis.This leads to an approximation result for the maximum of local averages through a Gaussian random field which preserves the covariance structure.

On manifold data spaces, we introduce a new family of location statistics describing centers of isotropic diffusion for different diffusion times. In contrast to the situation in Euclidean data, these diffusion means on manifolds do not generally coincide for different diffusion times. In the limit of vanishing diffusion time, diffusion means can be shown to converge to the intrinsic mean in general. For diverging diffusion time, we show for the circle and spheres of arbitrary dimension that diffusion means converge to the extrinsic mean in the canonical embedding into Euclidean space. The generalization of this result to real projective spaces leads to a conjecture for all compact symmetric spaces.