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
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| DC Element | Wert | Sprache |
|---|---|---|
| dc.contributor.advisor | Prof. Dr. Hanna Döring | ger |
| dc.creator | Betken, Carina | - |
| dc.date.accessioned | 2019-05-17T09:04:45Z | - |
| dc.date.available | 2019-05-17T09:04:45Z | - |
| dc.date.issued | 2019-05-17T09:04:47Z | - |
| dc.identifier.uri | https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-201905171547 | - |
| dc.description.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. | eng |
| dc.rights | Attribution 3.0 Germany | * |
| dc.rights.uri | http://creativecommons.org/licenses/by/3.0/de/ | * |
| dc.subject | preferential attachment random graphs | eng |
| dc.subject | Stein's method | eng |
| dc.subject | limiting distribution | eng |
| dc.subject | rates of convergence | eng |
| dc.subject | coupling | eng |
| dc.subject | power-law distribution | eng |
| dc.subject.ddc | 510 - Mathematik | ger |
| dc.title | Limit theorems in preferential attachment random graphs | eng |
| dc.type | Dissertation oder Habilitation [doctoralThesis] | - |
| thesis.location | Osnabrück | - |
| thesis.institution | Universität | - |
| thesis.type | Dissertation [thesis.doctoral] | - |
| thesis.date | 2019-05-03 | - |
| dc.contributor.referee | Prof. Dr. Adrian Röllin | ger |
| dc.subject.bk | 31.70 - Wahrscheinlichkeitsrechnung | ger |
| Enthalten in den Sammlungen: | FB06 - E-Dissertationen | |
Dateien zu dieser Ressource:
| Datei | Beschreibung | Größe | Format | |
|---|---|---|---|---|
| thesis_betken.pdf | Präsentationsformat | 1,42 MB | Adobe PDF | thesis_betken.pdf  Öffnen/Anzeigen |
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