Weighted Poisson–Delaunay mosaics

H. Edelsbrunner, A. Nikitenko, Theory of Probability and Its Applications 64 (2020) 595–614.


Journal Article | Published | English
Department
Abstract
Slicing a Voronoi tessellation in ${R}^n$ with a $k$-plane gives a $k$-dimensional weighted Voronoi tessellation, also known as a 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 generated by a Poisson point process in ${R}^n$, we study the expected number of simplices in the $k$-dimensional weighted Delaunay mosaic as well as the expected number of intervals of the Morse function, both as functions of a radius threshold. As a by-product, we obtain a new proof for the expected number of connected components (clumps) in a line section of a circular Boolean model in ${R}^n$.
Publishing Year
Date Published
2020-02-13
Journal Title
Theory of Probability and its Applications
Volume
64
Issue
4
Page
595-614
ISSN
eISSN
IST-REx-ID

Cite this

Edelsbrunner H, Nikitenko A. Weighted Poisson–Delaunay mosaics. Theory of Probability and its Applications. 2020;64(4):595-614. doi:10.1137/S0040585X97T989726
Edelsbrunner, H., & Nikitenko, A. (2020). Weighted Poisson–Delaunay mosaics. Theory of Probability and Its Applications, 64(4), 595–614. https://doi.org/10.1137/S0040585X97T989726
Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay Mosaics.” Theory of Probability and Its Applications 64, no. 4 (2020): 595–614. https://doi.org/10.1137/S0040585X97T989726.
H. Edelsbrunner and A. Nikitenko, “Weighted Poisson–Delaunay mosaics,” Theory of Probability and its Applications, vol. 64, no. 4, pp. 595–614, 2020.
Edelsbrunner H, Nikitenko A. 2020. Weighted Poisson–Delaunay mosaics. Theory of Probability and its Applications. 64(4), 595–614.
Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay Mosaics.” Theory of Probability and Its Applications, vol. 64, no. 4, SIAM, 2020, pp. 595–614, doi:10.1137/S0040585X97T989726.

Link(s) to Main File(s)
Access Level
OA Open Access

Export

Marked Publications

Open Data IST Research Explorer

Sources

arXiv 1705.08735

Search this title in

Google Scholar