Random Growth Processes on Graphs

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dc.contributor.advisor Zerner, Martin (Prof. Dr.)
dc.contributor.author Braun, Georg
dc.date.accessioned 2022-08-03T12:44:52Z
dc.date.available 2022-08-03T12:44:52Z
dc.date.issued 2022-10-01
dc.identifier.uri http://hdl.handle.net/10900/129867
dc.identifier.uri http://nbn-resolving.de/urn:nbn:de:bsz:21-dspace-1298672 de_DE
dc.identifier.uri http://dx.doi.org/10.15496/publikation-71229
dc.description.abstract In the present thesis, we consider three different random graph-theoretic growth models. These models are called ballistic deposition on finite graphs, Boolean percolation on directed graphs, and supercritical Galton-Watson branching processes with emigration. For our ballistic deposition model on finite graphs, we obtain various results, which characterize the relationship between the asymptotic growth rate and the underyling graph. Moreover, we prove that the fluctuations around this growth rate always satisfy a central limit theorem. In the context of Boolean percolation, we clarify under which conditions all but finitely many points of the graphs N_0^n and Z^n are covered. We also prove, for n ≥ 2, that it is impossible to cover the directed n-ary tree in this model. Besides, we present connections between this percolation model and the so-called random exchange process. Finally, we study under which conditions supercritical branching processes with emigration become extinct almost surely, and whether the expected survival time is finite. We investigate the extinction probability in relation to the population size, and the asymptotic growth of the population. To some extent, supercritical branching processes with emigration behave similarly to subcritical branching processes with immigration. en
dc.language.iso en de_DE
dc.publisher Universität Tübingen de_DE
dc.rights ubt-podok de_DE
dc.rights.uri http://tobias-lib.uni-tuebingen.de/doku/lic_mit_pod.php?la=de de_DE
dc.rights.uri http://tobias-lib.uni-tuebingen.de/doku/lic_mit_pod.php?la=en en
dc.subject.ddc 510 de_DE
dc.subject.other Verzweigungsprozesse de_DE
dc.subject.other Branching process en
dc.subject.other Autoregressive Prozesse de_DE
dc.subject.other Autoregressive Process en
dc.subject.other ballistic growth en
dc.subject.other ballistisches Wachstum de_DE
dc.subject.other Boolean percolation en
dc.subject.other Boolesche Perkolation de_DE
dc.title Random Growth Processes on Graphs en
dc.type Dissertation de_DE
dcterms.dateAccepted 2022-04-29
utue.publikation.fachbereich Mathematik de_DE
utue.publikation.fakultaet 7 Mathematisch-Naturwissenschaftliche Fakultät de_DE
utue.publikation.noppn yes de_DE


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