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

Show full item record

Google ScholarTM

Check

Altmetric