Concentration Inequalities for Poisson Functionals

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https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2016011313874
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dc.contributor.advisorProf. Dr. Matthias Reitzner
dc.creatorBachmann, Sascha
dc.date.accessioned2016-01-13T14:27:11Z
dc.date.available2016-01-13T14:27:11Z
dc.date.issued2016-01-13T14:27:11Z
dc.identifier.urihttps://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2016011313874-
dc.description.abstractIn 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.eng
dc.subjectPoisson Point Processeng
dc.subjectRandom Graphseng
dc.subjectConcentration Inequalitieseng
dc.subjectLogarithmic Sobolev Inequalitieseng
dc.subjectConvex Distanceeng
dc.subjectStochastic Geometryeng
dc.subjectSubgraph Countseng
dc.subjectComponent Countsger
dc.subject.ddc510 - Mathematik
dc.titleConcentration Inequalities for Poisson Functionalseng
dc.typeDissertation oder Habilitation [doctoralThesis]-
thesis.locationOsnabrück-
thesis.institutionUniversität-
thesis.typeDissertation [thesis.doctoral]-
thesis.date2015-12-10-
dc.contributor.refereeProf. Dr. Peter Eichelsbacher
dc.subject.msc60D05 - Geometric probability, stochastic geometry, random sets
vCard.ORGFB6
Enthalten in den Sammlungen:FB06 - E-Dissertationen

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