Concentration Inequalities for Poisson Functionals
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https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2016011313874
https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2016011313874
| Title: | Concentration Inequalities for Poisson Functionals |
| Authors: | Bachmann, Sascha |
| Thesis advisor: | Prof. Dr. Matthias Reitzner |
| Thesis referee: | Prof. Dr. Peter Eichelsbacher |
| Abstract: | In this thesis, new methods for proving concentration inequalities for Poisson functionals are developed. The focus is on techniques that are based on logarithmic Sobolev inequalities, but also results that are based on the convex distance for Poisson processes are presented. The general methods are applied to a variety of functionals associated with random geometric graphs. In particular, concentration inequalities for subgraph and component counts are proved. Finally, the established concentration results are used to derive strong laws of large numbers for subgraph and component counts associated with random geometric graphs. |
| URL: | https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2016011313874 |
| Subject Keywords: | Poisson Point Process; Random Graphs; Concentration Inequalities; Logarithmic Sobolev Inequalities; Convex Distance; Stochastic Geometry; Subgraph Counts; Component Counts |
| Issue Date: | 13-Jan-2016 |
| Type of publication: | Dissertation oder Habilitation [doctoralThesis] |
| Appears in Collections: | FB06 - E-Dissertationen |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| thesis_bachmann.pdf | Präsentationsformat | 1,59 MB | Adobe PDF | thesis_bachmann.pdf  View/Open |
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