--- res: bibo_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.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Herbert foaf_name: Edelsbrunner, Herbert foaf_surname: Edelsbrunner foaf_workInfoHomepage: http://www.librecat.org/personId=3FB178DA-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-9823-6833 - foaf_Person: foaf_givenName: Anton foaf_name: Nikitenko, Anton foaf_surname: Nikitenko foaf_workInfoHomepage: http://www.librecat.org/personId=3E4FF1BA-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-0659-3201 - foaf_Person: foaf_givenName: Matthias foaf_name: Reitzner, Matthias foaf_surname: Reitzner bibo_doi: 10.1017/apr.2017.20 bibo_issue: '3' bibo_volume: 49 dct_date: 2017^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/00018678 dct_language: eng dct_publisher: Cambridge University Press@ dct_title: Expected sizes of poisson Delaunay mosaics and their discrete Morse functions@ ...