Geometry of infinite clusters in continuum percolation models with strong correlations

Description

In the last ten years tremendous progress has been achieved in under- standing 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 proposal concerns the large-scale geometry of infinite connected components in specific models and in general systems. The main focus will lie on the development of new tools to address difficulties intrinsic to continuum models.

Preprints/Publications

Yingxin Mu, Artem Sapozhnikov: Visibility in Brownain interlacements, Poisson cylinders and Boolean models (04/2023)

Yingxin Mu, Artem Sapozhnikov: On questions of uniqueness for the vacant set of Wiener sausages and Brownian interlacements (04/2023)

Yingxin Mu, Artem Sapozhnikov: Uniqueness of the infinite connected component for the vacant set of random interlacements on amenable transient graphs (04/2023)

Members

  • member's portrait

    Prof. Dr. Artem Sapozhnikov

    Universit├Ąt Leipzig
    Principal Investigator
  • member's portrait

    Dr. Yingxin Mu

    Universit├Ąt Leipzig
    Associated Scientist

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