Decomposition of gamma-distributed domains constructed from Poisson point processes

R. Cowan, M. Quine, S. Zuev

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


A known gamma-type result for the Poisson process states that certain domains defined through configuration of the points (or 'particles') of the process have volumes which are gamma distributed. By proving the corresponding sequential gamma-type result, we show that in some cases such a domain allows for decomposition into subdomains each having independent exponentially distributed volumes. We consider other examples - based on the Voronoi and Delaunay tessellations - where a natural decomposition does not produce subdomains with exponentially distributed volumes. A simple algorithm for the construction of a typical Voronoi flower arises in this work. In our theoretical development, we generalize the classical theorem of Slivnyak, relating it to the strong Markov property of the Poisson process and to a result of Mecke and Muche (1995). This new theorem has interest beyond the specific problems being considered here.
Original languageEnglish
Pages (from-to)56-69
Number of pages13
JournalAdvances in Applied Probability
Issue number1
Publication statusPublished - 2003


  • stopping set
  • gamma-type results
  • slivnyak theorem
  • voronoi tessellation
  • delaunay triangulation
  • poisson process
  • statistics


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