Concentration Inequalities for Poisson Functionals

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Titel: Concentration Inequalities for Poisson Functionals
Autor(en): Bachmann, Sascha
Erstgutachter: Prof. Dr. Matthias Reitzner
Zweitgutachter: Prof. Dr. Peter Eichelsbacher
Zusammenfassung: 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://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2016011313874
Schlagworte: Poisson Point Process; Random Graphs; Concentration Inequalities; Logarithmic Sobolev Inequalities; Convex Distance; Stochastic Geometry; Subgraph Counts; Component Counts
Erscheinungsdatum: 13-Jan-2016
Enthalten in den Sammlungen:FB06 - E-Dissertationen

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