arXiv subjects

Kinga Nagy

Publications and source records attributed to Kinga Nagy.

4 recordsLinked to original sources

arXiv2026

Planarity and number of crossings in general models of random geometric graphs

Consider a random geometric graph with vertices given by a Poisson point process, and whose edges depend on independent marks corresponding to the vertices and pairs of vertices. In this paper, we study two related questions on this general model: the number of edge crossings in a projection of this graph, and its graph-theoretical planarity. We focus on models with heavy-tailed mark distributions, in particular with polynomial tails with arbitrary exponents. We show that the asymptotic behaviour varies significantly depending on this exponent.

math.PR↗

arXiv2025

On the Maximal Dimension of Random Simplicial Complexes

The dimension of random simplicial complexes (defined as the maximal dimension among all faces) is a natural extreme value associated with the complex, and is closely related to other functionals defined by a maximum, such as the clique number of geometric graphs or scan statistics. We extend existing results in the binomial point process case to the Poisson setting in sparse graphs, give new ones about expectations and large deviation principles in all regimes, as well as give a first precise distribution result in the dense case.

math.PR↗

arXiv2025

Existence of a plane without edge crossings in projections of the random geometric graph

Consider a random geometric graph $G$ with a vertex set defined by a Poisson point process with intensity $t>0$ in a convex body. We can generate a drawing of the graph by projecting the construction onto some plane $L$. Choosing different planes leads to different drawings, and in particular, potentially more or fewer edge crossings. In this paper, we prove that if the connection radius is smaller than a given threshold, the probability that there exists a plane with zero crossings tends to one as $t\to \infty$. We also state the asymptotic probability that such a plane is found after considering a given number of randomly chosen planes.

math.PR↗

arXiv2021

Monohedral Tilings of a Convex Disc with a Smooth Boundary

In this paper we give a complete description about normal monohedral tilings of a convex disc with smooth boundary where we have at most three topological discs as tiles. This result is a far-reaching generalization of the results of Kurusa, Lángi and Vígh \cite{KLV2020}. Some further partial results are proved for non-normal tilings.

math.MG↗