Universität zu Köln

Lüchtrath, Lukas ORCID: 0000-0003-4969-806X (2022). Percolation in weight-dependent random connection models. PhD thesis, Universität zu Köln.

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Abstract

We study a general class of inhomogeneous spatial random graphs, the weight-dependent random connection model. Vertices are given through a standard Poisson point process in Euclidean space and each vertex carries additionally an i.i.d weight. Edges are drawn in such a way that short edges and edges to large weight vertices are preferred. This allows in particular the study of models that combine long-range interactions and heavy-tailed degree distributions. The occurrence of long edges together with the hierarchy of the vertices coming from the weights typically leads to very well connected graphs. We identify a sharp phase transition where the existence of a subcritical percolation phase becomes possible. This transition depends on both, the power-law of the degree distribution and on the geometric model parameter, showing the significant effect of clustering on the graph’s topology. We further study the specifics of dimension one in parameter regimes where a subcritical phase exists. Natural examples that are contained in our framework are for instance the random connection model, the Poisson Boolean model, scale-free percolation and the agedependent random connection model. We use our results to characterize robustness of age-based spatial preferential attachment networks.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Lüchtrath, Lukas luechtrath@icloud.com orcid.org/0000-0003-4969-806X UNSPECIFIED
URN:	urn:nbn:de:hbz:38-640646
Date:	2022
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	Mathematics
Uncontrolled Keywords:	Keywords Language phase transition, spatial random graphs, schale-free random graphs, soft Boolean model, age-dependent random connection model, preferential attachment, robustness UNSPECIFIED
Date of oral exam:	31 October 2022
Referee:	Name Academic Title Mörters, Peter Prof. Dr. Komjáthy, Júlia Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/64064