Weighted Poisson–Delaunay mosaics Edelsbrunner, Herbert ; https://orcid.org/0000-0002-9823-6833 Nikitenko, Anton ; https://orcid.org/0000-0002-0659-3201 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 ${R}^n$. SIAM 2020 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/7554 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1137/S0040585X97T989726 info:eu-repo/semantics/altIdentifier/issn/0040-585X info:eu-repo/semantics/altIdentifier/e-issn/1095-7219 info:eu-repo/semantics/altIdentifier/wos/000551393100007 info:eu-repo/semantics/altIdentifier/arxiv/1705.08735 info:eu-repo/semantics/openAccess