Radius functions on Poisson–Delaunay mosaics and related complexes experimentally Abel Symposia Edelsbrunner, Herbert ; https://orcid.org/0000-0002-9823-6833 Nikitenko, Anton ; https://orcid.org/0000-0002-0659-3201 Ölsböck, Katharina ; https://orcid.org/0000-0002-4672-8297 Synak, Peter ddc:510 Discrete Morse theory has recently lead to new developments in the theory of random geometric complexes. This article surveys the methods and results obtained with this new approach, and discusses some of its shortcomings. It uses simulations to illustrate the results and to form conjectures, getting numerical estimates for combinatorial, topological, and geometric properties of weighted and unweighted Delaunay mosaics, their dual Voronoi tessellations, and the Alpha and Wrap complexes contained in the mosaics. Springer Nature 2020 info:eu-repo/semantics/conferenceObject doc-type:conferenceObject text http://purl.org/coar/resource_type/c_5794 https://research-explorer.ista.ac.at/record/8135 https://research-explorer.ista.ac.at/download/8135/8628 Edelsbrunner H, Nikitenko A, Ölsböck K, Synak P. Radius functions on Poisson–Delaunay mosaics and related complexes experimentally. In: <i>Topological Data Analysis</i>. Vol 15. Springer Nature; 2020:181-218. doi:<a href="https://doi.org/10.1007/978-3-030-43408-3_8">10.1007/978-3-030-43408-3_8</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-030-43408-3_8 info:eu-repo/semantics/altIdentifier/issn/2193-2808 info:eu-repo/semantics/altIdentifier/e-issn/2197-8549 info:eu-repo/semantics/altIdentifier/isbn/9783030434076 info:eu-repo/semantics/altIdentifier/wos/001321861000008 info:eu-repo/semantics/openAccess