article published yes Herbert Edelsbrunner author 3FB178DA-F248-11E8-B48F-1D18A9856A870000-0002-9823-6833 Anton Nikitenko author 3E4FF1BA-F248-11E8-B48F-1D18A9856A870000-0002-0659-3201 HeEd department Alpha Shape Theory Extended project Persistence and stability of geometric complexes project 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 ${R}^n$. SIAM2020 eng 0040-585X 1095-7219 1705.08735 00055139310000710.1137/S0040585X97T989726 644595-614 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>. 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> 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. H. Edelsbrunner, A. Nikitenko, Theory of Probability and Its Applications 64 (2020) 595–614. 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>. Edelsbrunner H, Nikitenko A. 2020. Weighted Poisson–Delaunay mosaics. Theory of Probability and its Applications. 64(4), 595–614. 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> 75542020-03-01T23:00:39Z2025-07-10T11:54:44Z