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1 results

  • The iteration of random tessellations and a construction of a homogeneous process of cell divisions

  • Part of
  • Joseph Mecke, Werner Nagel, Viola Weiss
  • Journal:
    Advances in Applied Probability / Volume 40 / Issue 1 / March 2008
    Published online by Cambridge University Press:
    01 July 2016, pp. 49-59
    Print publication:
    March 2008
    • Article
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  • A random tessellation of ℝd is said to be homogeneous if its distribution is invariant under all shifts of ℝd. The iteration of homogeneous random tessellations is described in a new manner that makes it evident that the resulting random tessellation is homogeneous again. Furthermore, a tessellation-valued process is constructed, the random states of which are homogeneous random tessellations stable under iteration (STIT). It can be interpreted as a process of subsequent division of cells.