منابع مشابه
Weighted Poisson–Delaunay Mosaics∗
Slicing a Voronoi tessellation in R 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 the smallest empty circumscribed sphere whose center lies in the k-plane gives a generalized discrete Morse function. Assuming the Voronoi tessellation is generate...
متن کاملVertex Numbers of Weighted Faces in Poisson Hyperplane Mosaics
In the random mosaic generated by a stationary Poisson hyperplane process in R, we consider the typical k-face weighted by the j-dimensional volume of the j-skeleton (0 ≤ j ≤ k ≤ d). We prove sharp lower and upper bounds for its expected number of vertices.
متن کاملRandom Inscribed Polytopes Have Similar Radius Functions as Poisson–Delaunay Mosaics∗
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 determine the expected number of intervals whose radii are less than or equal to a given threshold. Assuming the points are not contained in a hemisphere, t...
متن کاملExpected Sizes of Poisson–Delaunay Mosaics and Their Discrete Morse Functions∗
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 a Poisson point process in R, we study the expected number of simplices in the Delaunay mosaic as well as the expected number of critical simplices and non-singular intervals in the corresponding generalized d...
متن کاملLarge Cells in Poisson-Delaunay Tessellations
It is proved that the shape of the typical cell of a Delaunay tessellation, derived from a stationary Poisson point process in d-dimensional Euclidean space, tends to the shape of a regular simplex, given that the volume of the typical cell tends to infinity. This follows from an estimate for the probability that the typical cell deviates by a given amount from regularity, given that its volume...
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ژورنال
عنوان ژورنال: Теория вероятностей и ее применения
سال: 2019
ISSN: 0040-361X,2305-3151
DOI: 10.4213/tvp5196