Concentration bounds for geometric Poisson functionals: Logarithmic Sobolev inequalities revisited
Autor(en): | Bachmann, Sascha Peccati, Giovanni |
Stichwörter: | concentration of measure; CONSTANTS; convex distance; Herbst argument; LIMIT; logarithmic Sobolev inequalities; Mathematics; Poisson measure; random graphs; Statistics & Probability; stochastic geometry; U-STATISTICS | Erscheinungsdatum: | 2016 | Herausgeber: | UNIV WASHINGTON, DEPT MATHEMATICS | Journal: | ELECTRONIC JOURNAL OF PROBABILITY | Volumen: | 21 | Zusammenfassung: | We prove new concentration estimates for random variables that are functionals of a Poisson measure defined on a general measure space. Our results are specifically adapted to geometric applications, and are based on a pervasive use of a powerful logarithmic Sobolev inequality proved by L. Wu [43], as well as on several variations of the so-called Herbst argument. We provide several applications, in particular to edge counting and more general length power functionals in random geometric graphs, as well as to the convex distance for random point measures recently introduced by M. Reitzner [30]. |
ISSN: | 10836489 | DOI: | 10.1214/16-EJP4235 |
Zur Langanzeige