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.
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Drewitz, A., Ráth, B., Sapozhnikov, A. (2014). Source of Correlations and Decorrelation via Coupling. In: An Introduction to Random Interlacements. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-05852-8_7
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DOI: https://doi.org/10.1007/978-3-319-05852-8_7
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