{"date_created":"2020-03-01T23:00:39Z","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 ${R}^n$."}],"volume":64,"scopus_import":"1","_id":"7554","oa":1,"publication_status":"published","publication":"Theory of Probability and its Applications","language":[{"iso":"eng"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","isi":1,"article_processing_charge":"No","day":"13","publisher":"SIAM","department":[{"_id":"HeEd"}],"status":"public","external_id":{"isi":["000551393100007"],"arxiv":["1705.08735"]},"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833"},{"full_name":"Nikitenko, Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0659-3201","first_name":"Anton","last_name":"Nikitenko"}],"oa_version":"Preprint","date_updated":"2023-08-18T06:45:48Z","article_type":"original","type":"journal_article","doi":"10.1137/S0040585X97T989726","page":"595-614","issue":"4","title":"Weighted Poisson–Delaunay mosaics","quality_controlled":"1","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","call_identifier":"H2020","name":"Alpha Shape Theory Extended"},{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1705.08735"}],"intvolume":"        64","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>","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.","short":"H. Edelsbrunner, A. Nikitenko, Theory of Probability and Its Applications 64 (2020) 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>.","ista":"Edelsbrunner H, Nikitenko A. 2020. Weighted Poisson–Delaunay mosaics. Theory of Probability and its Applications. 64(4), 595–614.","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>."},"date_published":"2020-02-13T00:00:00Z","month":"02","ec_funded":1,"year":"2020","publication_identifier":{"issn":["0040585X"],"eissn":["10957219"]}}