Inhomogeneous spatial networks - beyond the weak decay regime


Description Phase 2

Complex Networks arise throughout the sciences wherever large systems of interacting objects are investigated. In this project we study a rich class of mathematical network models that satsify three basic principles: scale-freeness, the small-world property and clustering. To generate the models we form graphs consisting of randomly distributed vertices equipped with a weight, which are then connected by edges. The generation of each edge takes into account both the spatial distance between its endvertices as well as their weight. Our goal is to understand the behaviour of these models by answering questions such as: When are there large connected components? What are their topological properties, e.g. connectivity and interpoint graph distances? Do they qualitatively behave more like lattices or more like trees? And what happens if we randomly remove edges from them?

Preprints/Publications

Lukas Lüchtrath, Christian Mönch: Maximising homomorphism counts between digraphs (03/2026)

Lukas Lüchtrath, Christian Mönch: Age-dependent random connection models with arc reciprocity: clustering and connectivity (03/2026)

Lisa Hartung, Andreas Klippel, Christian Mönch: Extremes of the zero-average Gaussian Free Field on random regular graphs (11/2025)

Stein Andreas Bethuelsen, Christian Mönch: Strict monotonicity of critical points in independent long-range percolation models (10/2025)

Benedikt Jahnel, Lukas Lüchtrath, Christian Mönch: Phase transitions for contact processes on sparse random graphs via metastability and local limits (05/2025)

Andreas Klippel, Benjamin Lees, Christian Mönch: Loop vs. Bernoulli percolation on trees: strict inequality of critical values (03/2025)

Benedikt Jahnel, Lukas Lüchtrath, Christian Mönch: Phase transitions for contact processes on one-dimensional networks (01/2025)

Christian Mönch: Inhomogeneous long-range percolation in the strong decay regime: recurrence in one dimension (08/2024)

Lukas Lüchtrath, Christian Mönch: A very short proof of Sidorenko's inequality for counts of homomorphism between graphs (08/2024) published

Lisa Hartung, Christian Mönch, Florian Völlering: The mean field stubborn voter model (05/2024)

Christian Mönch: Inhomogeneous long-range percolation in the weak decay regime (03/2023) published

Members

  • member's portrait

    Dr. Christian Mönch

    Johannes Gutenberg-Universität Mainz
    Principal Investigator

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