Geometry of infinite clusters in continuum percolation models with strong correlations

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In the last ten years tremendous progress has been achieved in understanding lattice models of percolation with strong correlations, both in particular examples such as random interlacements as well as in general systems. The objects of this research proposal are percolation models in continuum with long-range spatial correlations. Some examples are the Boolean model, the Brownian interlacements, the Poisson cylinders and their vacant sets. The main focus will lie on the development of new tools to address difficulties intrinsic to continuum models.