Limit theorems in preferential attachment random graphs

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https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-201905171547
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Titel: Limit theorems in preferential attachment random graphs
Autor(en): Betken, Carina
Erstgutachter: Prof. Dr. Hanna Döring
Zweitgutachter: Prof. Dr. Adrian Röllin
Zusammenfassung: We consider a general preferential attachment model, where the probability that a newly arriving vertex connects to an older vertex is proportional to a (sub-)linear function of the indegree of the older vertex at that time. We provide a limit theorem with rates of convergence for the distribution of a vertex, chosen uniformly at random, as the number of vertices tends to infinity. To do so, we develop Stein's method for a new class of limting distributions including power-laws. Similar, but slightly weaker results are shown to be deducible using coupling techniques. Concentrating on a specific preferential attachment model we also show that the outdegree distribution asymptotically follows a Poisson law. In addition, we deduce a central limit theorem for the number of isolated vertices. We thereto construct a size-bias coupling which in combination with Stein’s method also yields bounds on the distributional distance.
URL: https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-201905171547
Schlagworte: preferential attachment random graphs; Stein's method; limiting distribution; rates of convergence; coupling; power-law distribution
Erscheinungsdatum: 17-Mai-2019
Lizenzbezeichnung: Attribution 3.0 Germany
URL der Lizenz: http://creativecommons.org/licenses/by/3.0/de/
Publikationstyp: Dissertation oder Habilitation [doctoralThesis]
Enthalten in den Sammlungen:FB06 - E-Dissertationen

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