A5069029768- Point processes and geometric inequalities
- Computational Geometry and Mesh Generation
- Mathematics and Applications
- Geometric Analysis and Curvature Flows
- Morphological variations and asymmetry
- Advanced Numerical Analysis Techniques
- Digital Image Processing Techniques
- Mathematical Approximation and Integration
- Diffusion and Search Dynamics
- graph theory and CDMA systems
- Analytic and geometric function theory
- Optimization and Packing Problems
- Geometry and complex manifolds
- Quasicrystal Structures and Properties
- Geometric and Algebraic Topology
- Sustainable Development and Environmental Policy
- Limits and Structures in Graph Theory
- Linguistic research and analysis
- Prion Diseases and Protein Misfolding
- Mathematical Inequalities and Applications
- Linguistics, Language Diversity, and Identity
- Entomological Studies and Ecology
- Data Management and Algorithms
- Dermatological and Skeletal Disorders
- Markov Chains and Monte Carlo Methods
University of Szeged
2016-2025
Eötvös Loránd University
2018
Alfréd Rényi Institute of Mathematics
2016
University of Castilla-La Mancha
2016
Complejo Hospitalario Universitario de Toledo
2016
Western Kentucky University
2016
University College London
2016
Technical University of Cluj-Napoca
2016
University of Calgary
2008-2015
McMaster University
2009
Abstract We consider a probability model in which the hull of sample i.i.d. uniform random points from convex disc K is formed by intersection all translates another suitable fixed L that contain sample. Such an object called -polygon . assume both and have $$C^2_+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mo>+</mml:mo> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> smooth boundaries, we prove upper bounds on variance number vertices...
Let K be a d -dimensional convex body with twice continuously differentiable boundary and everywhere positive Gauss-Kronecker curvature. Denote by n the hull of points chosen randomly independently from according to uniform distribution. Matching lower upper bounds are obtained for orders magnitude variances s th intrinsic volumes V ( ) ∈ {1,…, }. Furthermore, strong laws large numbers proved . The essential tools economic cap covering theorem Bárány Larman, Efron-Stein jackknife inequality.
Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding="application/x-tex">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a convex body in alttext="double-struck upper R Superscript d"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:mi>d</mml:mi> </mml:msup>...
Abstract An r -hyperconvex body is a set in the d -dimensional Euclidean space 𝔼 that intersection of family closed balls radius . We prove analogue classical Blaschke–Santaló inequality for bodies, and we also establish stability version it. The other main result paper an reverse isoperimetric plane.
In this paper we generalize some of the classical results Rényi and Sulanke (1963), (1964) in context spindle convexity. A planar convex disc S is if it intersection congruent closed circular discs. The finitely many discs called a polygon. We prove asymptotic formulae for expectation number vertices, missed area, perimeter difference uniform random polygons contained sufficiently smooth disc.
Let K be a d-dimensional convex body and let K(n) the intersection of n halfspaces containing whose bounding hyperplanes are independent identically distributed. Under suitable distributional assumptions, we prove an asymptotic formula for expectation difference mean widths K, another number facets K(n). These results achieved by establishing result on weighted volume approximation 'dualizing' it using polarity.
For two convex discs K and L, we say that is L-convex (Lángi et al., Aequationes Math. 85(1–2) (2013), 41–67) if it equal to the intersection of all translates L contain K. In L-convexity, set plays a similar role as closed half-spaces do in classical notion convexity. We study following probability model: Let be C + 2 smooth such L-convex. Select n independent identically distributed uniform random points x 1 , … from K, consider ( ) . The polygon expectation number vertices f 0 missed area...
Let $K$ be a convex body in $\mathbb{R}^d$ which slides freely ball. $K^{(n)}$ denote the intersection of $n$ closed half-spaces containing whose bounding hyperplanes are independent and identically distributed according to certain prescribed probability distribution. We prove an asymptotic formula for expectation difference volumes $K$, upper bound on variance volume $K^{(n)}$. achieve these results by first proving similar statements weighted mean width approximations bodies that admit...
Abstract In this paper we prove asymptotic upper bounds on the variance of number vertices and missed area inscribed random disc-polygons in smooth convex discs whose boundary is C + 2 . We also consider a circumscribed variant probability model which disc approximated by intersection circles.