arXiv subjects

Á. G. Horváth

Publications and source records attributed to Á. G. Horváth.

4 recordsLinked to original sources

arXiv2012

Normally distributed probability measure on the metric space of norms

In this paper we propose a method to construct probability measures on the space of convex bodies with a given pushforward distribution. Concretely we show that there is a measure on the metric space of centrally symmetric convex bodies, which pushforward by the thinness mapping produces a probability measure of truncated normal distribution on the interval of its range. Improving the construction we give another (more complicated) one with the following additional properties; the neighborhoods have positive measure, the set of polytopes has zero measure and the set of smooth bodies has measure 1, respectively.

math.PR↗

arXiv2010

Formulas on hyperbolic volume

This paper collects some important formulas on hyperbolic volume. To determine concrete values of volume function is a very hard question requiring the knowledge of various methods. Our goal to give a non-elementary integral on the volume of the orthosceme (obtain it without using the Schläfli differential formula), using edge-lengthes as the only parameters.

math.MG↗

arXiv2010

Bounded representation and radial projections of bisectors in normed spaces

It is well known that the description of topological and geometric properties of bisectors in normed spaces is a non-trivial subject. In this paper we introduce the concept of bounded representation of bisectors in finite dimensional real Banach spaces. This useful notion combines the concepts of bisector and shadow boundary of the unit ball, both corresponding with the same spatial direction. The bounded representation visualizes the connection between the topology of bisectors and shadow boundaries (Lemma 1) and gives the possibility to simplify and to extend some known results on radial projections of bisectors. Our main result (Theorem 1) says that in the manifold case the topology of the closed bisector and the topology of its bounded representation are the same; they are closed, $(n-1)$-dimensional balls embedded in Euclidean $n$-space in the standard way.

math.GT↗

arXiv2009

Packing points into a unit cube in higher space

In this paper using the concept of the extended Hamming code we give a construction for dense packing of points at distance at least one in such unit cubes which dimension are a power of two.

math.MG↗