---
_id: '7554'
abstract:
- lang: eng
  text: 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 ${R}^n$.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
- first_name: Anton
  full_name: Nikitenko, Anton
  id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
  last_name: Nikitenko
  orcid: 0000-0002-0659-3201
citation:
  ama: Edelsbrunner H, Nikitenko A. Weighted Poisson–Delaunay mosaics. <i>Theory of
    Probability and its Applications</i>. 2020;64(4):595-614. doi:<a href="https://doi.org/10.1137/S0040585X97T989726">10.1137/S0040585X97T989726</a>
  apa: Edelsbrunner, H., &#38; Nikitenko, A. (2020). Weighted Poisson–Delaunay mosaics.
    <i>Theory of Probability and Its Applications</i>. SIAM. <a href="https://doi.org/10.1137/S0040585X97T989726">https://doi.org/10.1137/S0040585X97T989726</a>
  chicago: Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay
    Mosaics.” <i>Theory of Probability and Its Applications</i>. SIAM, 2020. <a href="https://doi.org/10.1137/S0040585X97T989726">https://doi.org/10.1137/S0040585X97T989726</a>.
  ieee: H. Edelsbrunner and A. Nikitenko, “Weighted Poisson–Delaunay mosaics,” <i>Theory
    of Probability and its Applications</i>, vol. 64, no. 4. SIAM, pp. 595–614, 2020.
  ista: Edelsbrunner H, Nikitenko A. 2020. Weighted Poisson–Delaunay mosaics. Theory
    of Probability and its Applications. 64(4), 595–614.
  mla: Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay Mosaics.”
    <i>Theory of Probability and Its Applications</i>, vol. 64, no. 4, SIAM, 2020,
    pp. 595–614, doi:<a href="https://doi.org/10.1137/S0040585X97T989726">10.1137/S0040585X97T989726</a>.
  short: H. Edelsbrunner, A. Nikitenko, Theory of Probability and Its Applications
    64 (2020) 595–614.
date_created: 2020-03-01T23:00:39Z
date_published: 2020-02-13T00:00:00Z
date_updated: 2025-07-10T11:54:44Z
day: '13'
department:
- _id: HeEd
doi: 10.1137/S0040585X97T989726
ec_funded: 1
external_id:
  arxiv:
  - '1705.08735'
  isi:
  - '000551393100007'
intvolume: '        64'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1705.08735
month: '02'
oa: 1
oa_version: Preprint
page: 595-614
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '788183'
  name: Alpha Shape Theory Extended
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: I02979-N35
  name: Persistence and stability of geometric complexes
publication: Theory of Probability and its Applications
publication_identifier:
  eissn:
  - 1095-7219
  issn:
  - 0040-585X
publication_status: published
publisher: SIAM
quality_controlled: '1'
scopus_import: '1'
status: public
title: Weighted Poisson–Delaunay mosaics
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 64
year: '2020'
...