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Item type:Publication, Access status: with files , The radial spanning tree in hyperbolic space: degree and edge-length*(Institute of Mathematical Statistics, 2025-08-07); ; ; Consider a stationary Poisson process η in a d-dimensional hyperbolic space of constant curvature −κ and let the points of η together with a fixed origin o be the vertices of a graph. Connect each point x ∈ η with its radial nearest neighbour, which is the hyperbolically nearest vertex to x that is closer to o than x. This construction gives rise to the hyperbolic radial spanning tree, whose geometric properties are in the focus of this paper. In particular, the degree of the origin is studied. For increasing balls around o as observation windows, expectation and variance asymptotics as well as a quantitative central limit theorem for a class of edge-length functionals are derived. The results are contrasted with those for the Euclidean radial spanning tree.Publicationtype: Journal Article17 24 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Normal approximation of Kabanov–Skorohod Integrals on poisson spaces(2024-06); ; We consider the normal approximation of Kabanov–Skorohod integrals on a general Poisson space. Our bounds are for the Wasserstein and the Kolmogorov distance and involve only difference operators of the integrand of the Kabanov–Skorohod integral. The proofs rely on the Malliavin–Stein method and, in particular, on multiple applications of integration by parts formulae. As examples, we study some linear statistics of point processes that can be constructed by Poisson embeddings and functionals related to Pareto optimal points of a Poisson process.Publicationtype: Journal ArticleScopus© Citations 1 27 63