Limit theorems in preferential attachment random graphs
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https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-201905171547
https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-201905171547
Title: | Limit theorems in preferential attachment random graphs |
Authors: | Betken, Carina |
Thesis advisor: | Prof. Dr. Hanna Döring |
Thesis referee: | Prof. Dr. Adrian Röllin |
Abstract: | 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 |
Subject Keywords: | preferential attachment random graphs; Stein's method; limiting distribution; rates of convergence; coupling; power-law distribution |
Issue Date: | 17-May-2019 |
License name: | Attribution 3.0 Germany |
License url: | http://creativecommons.org/licenses/by/3.0/de/ |
Type of publication: | Dissertation oder Habilitation [doctoralThesis] |
Appears in Collections: | FB06 - E-Dissertationen |
Files in This Item:
File | Description | Size | Format | |
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thesis_betken.pdf | Präsentationsformat | 1,42 MB | Adobe PDF | thesis_betken.pdf View/Open |
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