Random Geometric Structures
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https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-202001302552
https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-202001302552
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DC Element | Wert | Sprache |
---|---|---|
dc.contributor.advisor | Matthias Reitzner | ger |
dc.creator | Grygierek, Jens Jan | - |
dc.date.accessioned | 2020-01-30T09:50:33Z | - |
dc.date.available | 2020-01-30T09:50:33Z | - |
dc.date.issued | 2020-01-30T09:50:34Z | - |
dc.identifier.uri | https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-202001302552 | - |
dc.description.abstract | We construct and investigate random geometric structures that are based on a homogeneous Poisson point process. We investigate the random Vietoris-Rips complex constructed as the clique complex of the well known gilbert graph as an infinite random simplicial complex and prove that every realizable finite sub-complex will occur infinitely many times almost sure as isolated complex and also in the case of percolations connected to the unique giant component. Similar results are derived for the Cech complex. We derive limit theorems for the f-vector of the Vietoris-Rips complex on the unit cube centered at the origin and provide a central limit theorem and a Poisson limit theorem based on the model parameters. Finally we investigate random polytopes that are given as convex hulls of a Poisson point process in a smooth convex body. We establish a central limit theorem for certain linear combinations of intrinsic volumes. A multivariate limit theorem involving the sequence of intrinsic volumes and the number of i-dimensional faces is derived. We derive the asymptotic normality of the oracle estimator of minimal variance for estimation of the volume of a convex body. | eng |
dc.rights | Attribution 3.0 Germany | * |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/de/ | * |
dc.subject | Malliavin-Stein | eng |
dc.subject | random simplicial complex | eng |
dc.subject | random polytope | eng |
dc.subject | limit theorems | eng |
dc.subject | Poisson point process | eng |
dc.subject.ddc | 510 - Mathematik | ger |
dc.title | Random Geometric Structures | eng |
dc.type | Dissertation oder Habilitation [doctoralThesis] | - |
thesis.location | Osnabrück | - |
thesis.institution | Universität | - |
thesis.type | Dissertation [thesis.doctoral] | - |
thesis.date | 2020-01-22 | - |
orcid.creator | https://orcid.org/0000-0002-2709-2115 | - |
dc.contributor.referee | Matthias Schulte | ger |
dc.subject.msc | 60D05 - Geometric probability, stochastic geometry, random sets | ger |
Enthalten in den Sammlungen: | FB06 - E-Dissertationen |
Dateien zu dieser Ressource:
Datei | Beschreibung | Größe | Format | |
---|---|---|---|---|
thesis_grygierek.pdf | Präsentationsformat | 2,87 MB | Adobe PDF | thesis_grygierek.pdf Öffnen/Anzeigen |
Diese Ressource wurde unter folgender Copyright-Bestimmung veröffentlicht: Lizenz von Creative Commons