Electronic Journal of Probability
- Electron. J. Probab.
- Volume 21 (2016), paper no. 6, 44 pp.
Concentration bounds for geometric Poisson functionals: Logarithmic Sobolev inequalities revisited
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 , 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 .
Electron. J. Probab., Volume 21 (2016), paper no. 6, 44 pp.
Received: 14 April 2015
Accepted: 3 January 2016
First available in Project Euclid: 5 February 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Bachmann, Sascha; Peccati, Giovanni. Concentration bounds for geometric Poisson functionals: Logarithmic Sobolev inequalities revisited. Electron. J. Probab. 21 (2016), paper no. 6, 44 pp. doi:10.1214/16-EJP4235. https://projecteuclid.org/euclid.ejp/1454682887