Poisson Point Processes

  • Alexander Drewitz
  • Balázs Ráth
  • Artëm Sapozhnikov
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)


In this chapter we review the notion of a Poisson point process on a measurable space as well as some basic operations (coloring, mapping, thinning) that we will need for the construction of the random interlacement point process and in the study of its properties. First we recall some well-known facts about the Poisson distribution.


Poisson Point Process Random Interlacements Abstract Measurable Spaces Poisson Distribution Poisson Particle 
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    Resnick, S.I.: Extreme values, regular variation and point processes. In: Springer Series in Operations Research and Financial Engineering. Springer, New York (2008). Reprint of the 1987 originalGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Alexander Drewitz
    • 1
  • Balázs Ráth
    • 2
  • Artëm Sapozhnikov
    • 3
  1. 1.Department of MathematicsColumbia UniversityNew York CityUSA
  2. 2.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  3. 3.Max-Planck Institute of Mathematics in the SciencesLeipzigGermany

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