Random Interlacements: First Definition and Basic Properties

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


In this chapter we give the first definition of random interlacements at level u > 0 as a random subset of \({\mathbb{Z}}^{d}\). We then prove that it has polynomially decaying correlations and is invariant and ergodic with respect to the lattice shifts.


Random Subset Lattice Shift Poisson Point Process Graph Distance Simple Random Walk 
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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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