---
_id: '718'
abstract:
- lang: eng
text: 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 n , we study the expected
number of simplices in the Delaunay mosaic as well as the expected number of critical
simplices and nonsingular intervals in the corresponding generalized discrete
gradient. Observing connections with other probabilistic models, we obtain precise
expressions for the expected numbers in low dimensions. In particular, we obtain
the expected numbers of simplices in the Poisson–Delaunay mosaic in dimensions
n ≤ 4.
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
- first_name: Matthias
full_name: Reitzner, Matthias
last_name: Reitzner
citation:
ama: Edelsbrunner H, Nikitenko A, Reitzner M. Expected sizes of poisson Delaunay
mosaics and their discrete Morse functions. Advances in Applied Probability.
2017;49(3):745-767. doi:10.1017/apr.2017.20
apa: Edelsbrunner, H., Nikitenko, A., & Reitzner, M. (2017). Expected sizes
of poisson Delaunay mosaics and their discrete Morse functions. Advances in
Applied Probability. Cambridge University Press. https://doi.org/10.1017/apr.2017.20
chicago: Edelsbrunner, Herbert, Anton Nikitenko, and Matthias Reitzner. “Expected
Sizes of Poisson Delaunay Mosaics and Their Discrete Morse Functions.” Advances
in Applied Probability. Cambridge University Press, 2017. https://doi.org/10.1017/apr.2017.20.
ieee: H. Edelsbrunner, A. Nikitenko, and M. Reitzner, “Expected sizes of poisson
Delaunay mosaics and their discrete Morse functions,” Advances in Applied Probability,
vol. 49, no. 3. Cambridge University Press, pp. 745–767, 2017.
ista: Edelsbrunner H, Nikitenko A, Reitzner M. 2017. Expected sizes of poisson Delaunay
mosaics and their discrete Morse functions. Advances in Applied Probability. 49(3),
745–767.
mla: Edelsbrunner, Herbert, et al. “Expected Sizes of Poisson Delaunay Mosaics and
Their Discrete Morse Functions.” Advances in Applied Probability, vol.
49, no. 3, Cambridge University Press, 2017, pp. 745–67, doi:10.1017/apr.2017.20.
short: H. Edelsbrunner, A. Nikitenko, M. Reitzner, Advances in Applied Probability
49 (2017) 745–767.
date_created: 2018-12-11T11:48:07Z
date_published: 2017-09-01T00:00:00Z
date_updated: 2023-09-07T12:07:12Z
day: '01'
department:
- _id: HeEd
doi: 10.1017/apr.2017.20
ec_funded: 1
external_id:
arxiv:
- '1607.05915'
intvolume: ' 49'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1607.05915
month: '09'
oa: 1
oa_version: Preprint
page: 745 - 767
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Advances in Applied Probability
publication_identifier:
issn:
- '00018678'
publication_status: published
publisher: Cambridge University Press
publist_id: '6962'
quality_controlled: '1'
related_material:
record:
- id: '6287'
relation: dissertation_contains
status: public
scopus_import: 1
status: public
title: Expected sizes of poisson Delaunay mosaics and their discrete Morse functions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 49
year: '2017'
...