Coupling of Point Measures of Excursions

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


In this chapter we prove Theorem 8.3. It will follow from Theorem 7.9 as soon as we show that for some K 1 and K 2 such that \(G_{\mathcal{T}_{i}} \in \sigma (\varPsi _{z},\ z \in K_{i})\), and for a specific choice of \(U_{1},U_{2},S_{1},S_{2}\) satisfying () and (), there exists a coupling of point measures ζ ∗∗ (see ()) and ζ −, + (see ()) such that the condition () is satisfied with ε = ε(u , n), where ε(u , n) is defined in ().


Excursion Poisson Point Process Independent Poisson Random Variables Geometric Length Scale Dyadic Tree 
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  1. [44]
    Sznitman, A.S.: Decoupling inequalities and interlacement percolation on \(G \times \mathbb{Z}\). Invent. Math. 187(3), 645–706 (2012). DOI 10.1007/s00222-011-0340-9. URL

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© 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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