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pro vyhledávání: '"Nikitenko, Anton"'
The approximation of a circle with the edges of a fine square grid distorts the perimeter by a factor about $\tfrac{4}{\pi}$. We prove that this factor is the same on average (in the ergodic sense) for approximations of any rectifiable curve by the e
Externí odkaz:
http://arxiv.org/abs/2012.03350
Consider a random set of points on the unit sphere in $\mathbb{R}^d$, which can be either uniformly sampled or a Poisson point process. Its convex hull is a random inscribed polytope, whose boundary approximates the sphere. We focus on the case $d=3$
Externí odkaz:
http://arxiv.org/abs/2007.07783
Autor:
Nikitenko, Anton
In some applications, like some areas in stochastic geometry, a convenient change of variables involves spheres. In this review we summarize formulas of Blaschke-Petkantschin type, that help to pass from integration over $k$-tuples of points in space
Externí odkaz:
http://arxiv.org/abs/1904.10750
The order-$k$ Voronoi tessellation of a locally finite set $X \subseteq \mathbb{R}^n$ decomposes $\mathbb{R}^n$ into convex domains whose points have the same $k$ nearest neighbors in $X$. Assuming $X$ is a stationary Poisson point process, we give e
Externí odkaz:
http://arxiv.org/abs/1709.09380
Slicing a Voronoi tessellation in $\mathbb{R}^n$ with a $k$-plane gives a $k$-dimensional weighted Voronoi tessellation, also known as power diagram or Laguerre tessellation. Mapping every simplex of the dual weighted Delaunay mosaic to the radius of
Externí odkaz:
http://arxiv.org/abs/1705.08735
Publikováno v:
Annals of Applied Probability Volume 28, Number 5 (2018), 3215-3238
Using the geodesic distance on the $n$-dimensional sphere, we study the expected radius function of the Delaunay mosaic of a random set of points. Specifically, we consider the partition of the mosaic into intervals of the radius function and determi
Externí odkaz:
http://arxiv.org/abs/1705.02870
Akademický článek
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Publikováno v:
Advances in Applied Probability. 49 (2016)
Mapping every simplex in the Delaunay mosaic of a discrete point set to the radius of the smallest empty circumsphere gives a generalized discrete Morse function. Choosing the points from an n-dimensional Poisson point process, we study the expected
Externí odkaz:
http://arxiv.org/abs/1607.05915
Publikováno v:
Combinatorica (2016), pp. 1--24
We introduce the Voronoi functional of a triangulation of a finite set of points in the Euclidean plane and prove that among all geometric triangulations of the point set, the Delaunay triangulation maximizes the functional. This result neither exten
Externí odkaz:
http://arxiv.org/abs/1411.6337
Autor:
Musin, Oleg R., Nikitenko, Anton V.
Publikováno v:
Discrete Comput Geom (2016) 55: 1
We consider packings of congruent circles on a square flat torus, i.e., periodic (w.r.t. a square lattice) planar circle packings, with the maximal circle radius. This problem is interesting due to a practical reason - the problem of "super resolutio
Externí odkaz:
http://arxiv.org/abs/1212.0649