@article{7554,
  abstract     = {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 ${R}^n$.},
  author       = {Edelsbrunner, Herbert and Nikitenko, Anton},
  issn         = {1095-7219},
  journal      = {Theory of Probability and its Applications},
  number       = {4},
  pages        = {595--614},
  publisher    = {SIAM},
  title        = {{Weighted Poisson–Delaunay mosaics}},
  doi          = {10.1137/S0040585X97T989726},
  volume       = {64},
  year         = {2020},
}