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Large components in inhomogeneous random graphs

Citation Link: https://doi.org/10.15480/882.14939
Publikationstyp
Doctoral Thesis
Date Issued
2025
Sprache
English
Author(s)
Lienau, Matthias  
Advisor
Schulte, Matthias  
Referee
Hirsch, Christian
Title Granting Institution
Technische Universität Hamburg
Place of Title Granting Institution
Hamburg
Examination Date
2025-02-07
Institute
Mathematik E-10  
TORE-DOI
10.15480/882.14939
TORE-URI
https://hdl.handle.net/11420/54885
Citation
Technische Universität Hamburg (2025)
This thesis studies two types of inhomogeneous random graphs, so-called rank-1 models and the weighted random connection model. Under suitable parameter choices, both random graphs exhibit a scale-free degree distribution as observed in real-world complex networks. For both models, we study the sizes of large components in the subcritical regime. In the rank-1 case, we also establish quantitative Poisson approximation results for cycle counts. The latter allow us to deduce the asymptotic distributions of the lengths of the shortest and of the longest cycle in the subcritical regime.
Subjects
inhomogeneous random graphs
random connection model
(extremal) counting statistics
subcritical regime
power law
Poisson process convergence
DDC Class
519: Applied Mathematics, Probabilities
Lizenz
https://creativecommons.org/licenses/by/4.0/
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