Condensation in random geometric graphs

Description

In a random geometric graph points are randomly distributed in space, and each point is given a random radius. Two points are joined by an edge if their distance is smaller than the sum of the two radii. When such a random graph is conditioned to have more edges than it would normally have, the excess edges can form different geometries. For example, a small number of points could get a large radius and therefore be adjacent to a high number of edges, or points could accumulate in a small spatial area and form a complete graph by virtue of their proximity. The purpose of the project is to investigate the different geometric configurations arising in these condensing graphs in dependence on the distribution of the individual radii.

Preprints/Publications

Peter Gracar, Arne Grauer: The contact process on scale-free geometric random graphs (08/2022)

Céline Kerriou, Peter Mörters: The fewest-big-jumps principle and an application to random graphs (06/2022)

Peter Gracar, Arne Grauer, Peter Mörters: Chemical distance in geometric random graphs with long edges and scale-free degree distribution. (08/2021) published

Peter Gracar, Markus Heydenreich, Christian Mönch, Peter Mörters: Transience Versus Recurrence for Scale-Free Spatial Networks (09/2020) published

Peter Gracar, Lukas Lüchtrath, Peter Mörters: Percolation phase transition in weight-dependent random connection models. (03/2020)

Peter Gracar, Markus Heydenreich, Christian Mönch, Peter Mörters: Recurrence vs transience for weight-dependent random connection models. (11/2019) published

Members

  • member's portrait

    Prof. Dr. Peter Mörters

    Universität zu Köln
    Principal Investigator
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    M. Sc. Marilyn Düsterbeck

    Universität zu Köln
    Associated Scientist
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    M. Sc. Arne Grauer

    Universität zu Köln
    Associated Scientist
  • member's portrait

    M. Sc. Céline Kerriou

    Universität zu Köln
    Associated Scientist
  • member's portrait

    M. Sc. Lukas Luechtrath

    Weierstrass Institute
    Associated Scientist

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