---
res:
  bibo_abstract:
  - The main objects considered in the present work are simplicial and CW-complexes
    with vertices forming a random point cloud. In particular, we consider a Poisson
    point process in R^n and study Delaunay and Voronoi complexes of the first and
    higher orders and weighted Delaunay complexes obtained as sections of Delaunay
    complexes, as well as the Čech complex. Further, we examine theDelaunay complex
    of a Poisson point process on the sphere S^n, as well as of a uniform point cloud,
    which is equivalent to the convex hull, providing a connection to the theory of
    random polytopes. Each of the complexes in question can be endowed with a radius
    function, which maps its cells to the radii of appropriately chosen circumspheres,
    called the radius of the cell. Applying and developing discrete Morse theory for
    these functions, joining it together with probabilistic and sometimes analytic
    machinery, and developing several integral geometric tools, we aim at getting
    the distributions of circumradii of typical cells. For all considered complexes,
    we are able to generalize and obtain up to constants the distribution of radii
    of typical intervals of all types. In low dimensions the constants can be computed
    explicitly, thus providing the explicit expressions for the expected numbers of
    cells. In particular, it allows to find the expected density of simplices of every
    dimension for a Poisson point process in R^4, whereas the result for R^3 was known
    already in 1970's.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Anton
      foaf_name: Nikitenko, Anton
      foaf_surname: Nikitenko
      foaf_workInfoHomepage: http://www.librecat.org/personId=3E4FF1BA-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-0659-3201
  bibo_doi: 10.15479/AT:ISTA:th_873
  dct_date: 2017^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/2663-337X
  dct_language: eng
  dct_publisher: Institute of Science and Technology Austria@
  dct_title: Discrete Morse theory for random complexes @
...