Related papers: Negative dimension in general and asymptotic topol…
Asymptotic net is an important concept in discrete differential geometry. In this paper, we show that we can associate affine discrete geometric concepts to an arbitrary non-degenerate asymptotic net. These concepts include discrete affine…
We give a bound, linear in the complexity of the surface, on the asymptotic dimension of the curve complex as well as the capacity dimension of the ending lamination space.
The aim of this article is to analyze the asymptotic properties of the C-metric, using a general method specified in work of Tafel and coworkers, [1], [2], [3]. By finding an appropriate conformal factor $\Omega$, it allows the…
The positivity of the Bondi mass has been proven in 4 dimensions, but in higher dimensions the issue remains open. The formalism of the present paper has been developed to investigate this and is well suited to the higher dimensional case.…
Here we look at some geometric properties related to connectedness and topological dimension 0, especially in connection with norms on vector spaces over fields with absolute value functions, which may be non-archimedian.
Linear statistics of random zero sets are integrals of smooth differential forms over the zero set and as such are smooth analogues of the volume of the random zero set inside a fixed domain. We derive an asymptotic expansion for the…
For any ring we propose the construction of a cover which increases the finitistic dimension on one side and decreases the finitistic dimension to zero on the opposite side. This complements recent work of Cummings.
We introduce the notion of tiling spaces for metric spaces. The class of tiling spaces contains the Euclidean spaces, the middle-third Cantor set, and various self-similar spaces appearing in fractal geometry. For doubling tiling spaces, we…
In this manuscript, we provide a concise review of the concept of metric dimension for both deterministic as well as random graphs. Algorithms to approximate this quantity, as well as potential applications, are also reviewed. This work has…
Different viewpoints on the asymptotic expansion of Feynman diagrams are reviewed. The relations between the field theoretic and diagrammatic approaches are sketched. The focus is on problems with large masses or large external momenta.…
We construct families of asymptotically locally hyperbolic Riemannian metrics with constant scalar curvature (i.e., time symmetric vacuum general relativistic initial data sets with negative cosmological constant), with prescribed topology…
We explore the concept of negative pressure and its relevance in a variety of physical contexts: the expansion of the universe, mixture theory, cavitation, and the capillary effect in plants. Using thermodynamic arguments, we discuss the…
We review recent results concerning general properties of higher dimensional black holes. The topics selected with particular focus are those concerning topology, symmetry, and uniqueness properties of asymptotically flat vacuum black holes…
We study the topological complexities of relative entropy zero extensions acted by countableinfinite amenable groups. Firstly, for a given Folner sequence $\{F_n\}_{n=0}^\infty$, we define respectively the relative entropy dimensions and…
Let M be a complete Riemannian manifold with negative curvature, and let C_-, C_+ be two properly immersed closed convex subsets of M. We survey the asymptotic behaviour of the number of common perpendiculars of length at most s from C_- to…
This paper is devoted to the study of the topological pressure dimension for almost additive sequences, which is an extension of topological entropy dimension. We investigate fundamental properties of the topological pressure dimension for…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional condition on its rate of increase compared to the sample size. On the…
These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.
The notion of geometric version of an infinitely divisible law is introduced. Concepts parallel to attraction and partial attraction are developed and studied in the setup of geometric summing of random variables.
We study right limits of the Bergman Shift matrix. Our results have applications to ratio asymptotics, weak asymptotic measures, relative asymptotics, and zero counting measures of the orthogonal and orthonormal polynomials.