Concentration for Poisson functionals: Component counts in random geometric graphs

Autor(en): Bachmann, Sascha
Stichwörter: Component counts; Concentration inequalities; LOGARITHMIC SOBOLEV INEQUALITIES; Mathematics; Poisson point process; Random graphs; Statistics & Probability
Erscheinungsdatum: 2016
Herausgeber: ELSEVIER
Journal: STOCHASTIC PROCESSES AND THEIR APPLICATIONS
Volumen: 126
Ausgabe: 5
Startseite: 1306
Seitenende: 1330
Zusammenfassung: 
Upper bounds for the probabilities P(F >= EF r) and IP(F <= EF - r) are proved, where F is a certain component count associated with a random geometric graph built over a Poisson point process on R-d. The bounds for the upper tail decay exponentially, and the lower tail estimates even have a Gaussian decay. For the proof of the concentration inequalities, recently developed methods based on logarithmic Sobolev inequalities are used and enhanced. A particular advantage of this approach is that the resulting inequalities even apply in settings where the underlying Poisson process has infinite intensity measure. (C) 2015 Elsevier B.V. All rights reserved.
ISSN: 03044149
DOI: 10.1016/j.spa.2015.11.004

Show full item record

Google ScholarTM

Check

Altmetric