arXiv subjects

Balázs Grünfelder

Publications and source records attributed to Balázs Grünfelder.

3 recordsLinked to original sources

arXiv2026

Higher moments of intrinsic volumes of random beta-prime polytopes

We consider beta-prime polytopes, i.e., the convex hulls of iid random points chosen according to beta-prime distributions in $\mathbb{R}^d$. After suitable scaling, beta-prime polytopes converge in distribution to the convex hulls of Poisson point processes with power-law intensity functions. We prove moment convergence for the volume and all intrinsic volumes. Beta-prime polytopes are the push-forwards of spherical random polytopes on the upper open half-sphere of the unit sphere $S^d\subset \mathbb{R}^{d+1}$. We prove convergence of moments of the spherical volume difference of the half-sphere and the spherical random polytopes.

math.MG↗

arXiv2025

Variances and central limit theorems for random beta-polytopes and in other geometric models

We prove matching asymptotic lower and upper bounds on the variances of the intrinsic volumes and the number of $k$-faces of $d$-dimensional random beta-polytopes. Using Stein's methods, we establish central limit theorems for the intrinsic volumes. We also prove asymptotic upper bounds on the variances of the volume and vertex number of spherical random polytopes in spherical convex bodies, and hyperbolic random polytopes in convex bodies in hyperbolic space. Moreover, we consider a circumscribed model on the sphere.

math.MG↗

arXiv2021

Variance bounds for disc-polygons

We prove asymptotic lower bounds on the variance of the number of vertices and missed area of random disc-polygons in convex discs whose boundary is $C_+^2$ smooth. The established lower bounds are of the same order as the upper bounds proved previously by Fodor and V\'ıgh (2018).

math.MG↗