[{"quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/1705.08735","open_access":"1"}],"page":"595-614","publication":"Theory of Probability and its Applications","external_id":{"arxiv":["1705.08735"],"isi":["000551393100007"]},"department":[{"_id":"HeEd"}],"citation":{"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>","ista":"Edelsbrunner H, Nikitenko A. 2020. Weighted Poisson–Delaunay mosaics. Theory of Probability and its Applications. 64(4), 595–614.","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>.","short":"H. Edelsbrunner, A. Nikitenko, Theory of Probability and Its Applications 64 (2020) 595–614.","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.","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>.","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>"},"type":"journal_article","doi":"10.1137/S0040585X97T989726","publication_status":"published","abstract":[{"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 ${R}^n$.","lang":"eng"}],"article_processing_charge":"No","month":"02","intvolume":"        64","ec_funded":1,"scopus_import":"1","language":[{"iso":"eng"}],"issue":"4","arxiv":1,"title":"Weighted Poisson–Delaunay mosaics","publisher":"SIAM","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2025-07-10T11:54:44Z","day":"13","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","call_identifier":"FWF"}],"date_published":"2020-02-13T00:00:00Z","volume":64,"author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Nikitenko","orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton","first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87"}],"status":"public","isi":1,"_id":"7554","oa_version":"Preprint","year":"2020","article_type":"original","oa":1,"publication_identifier":{"issn":["0040-585X"],"eissn":["1095-7219"]},"date_created":"2020-03-01T23:00:39Z"}]