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Source of Correlations and Decorrelation via Coupling

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

Abstract

In this chapter we consider the question of correlations in random interlacements. We have already seen in Remark 2.6 that the random set \({\mathcal{I}}^{u}\) exhibits long-range correlations. Despite of this, we want to effectively control the stochastic dependence of locally defined events with disjoint (distant) support. We will identify the source of correlations in the model and use the trick of coupling to compare the correlated events to their decorrelated counterparts.

Keywords

Point Measure Exit Time Poisson Point Process Entrance Time Polynomial Decay 
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References

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    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 http://dx.doi.org/10.1007/s00222-011-0340-9
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    Teixeira, A.: Interlacement percolation on transient weighted graphs. Electron. J. Probab. 14(54), 1604–1628 (2009). DOI 10.1214/EJP.v14-670. URL http://dx.doi.org/10.1214/EJP.v14-670

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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