Expected sizes of poisson Delaunay mosaics and their discrete Morse functions Journal Article

Author(s): Edelsbrunner, Herbert; Nikitenko, Anton; Reitzner, Matthias
Article Title: Expected sizes of poisson Delaunay mosaics and their discrete Morse functions
Affiliation IST Austria
Abstract: 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.
Keywords: intervals; Integral geometry; Poisson point process; Delaunay mosaic; discrete Morse theory; critical simplices; stochastic geometry; typical simplex
Journal Title: Advances in Applied Probability
Volume: 49
Issue 3
ISSN: 1475-6064
Publisher: Cambridge University Press  
Date Published: 2017-01-01
Start Page: 745
End Page: 767
DOI: 10.1017/apr.2017.20
Notes: This work is partially supported by the Toposys project FP7-ICT-318493-STREP, by ESF under the ACAT Research Network Programme, and by the FWF within the SFB-Transregio Programme 109 in Discretization in Geometry and Dynamics (grant no. I02979-N35).
Open access: yes (repository)
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