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Concentration Inequalities for Poisson Functionals

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.

Identiferoai:union.ndltd.org:uni-osnabrueck.de/oai:repositorium.ub.uni-osnabrueck.de:urn:nbn:de:gbv:700-2016011313874
Date13 January 2016
CreatorsBachmann, Sascha
ContributorsProf. Dr. Matthias Reitzner, Prof. Dr. Peter Eichelsbacher
Source SetsUniversität Osnabrück
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:doctoralThesis
Formatapplication/pdf, application/zip
Rightshttp://rightsstatements.org/vocab/InC/1.0/

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