Electronic Journal of Probability

Concentration bounds for geometric Poisson functionals: Logarithmic Sobolev inequalities revisited

Abstract

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].

Article information

Source
Electron. J. Probab., Volume 21 (2016), paper no. 6, 44 pp.

Dates
Accepted: 3 January 2016
First available in Project Euclid: 5 February 2016

https://projecteuclid.org/euclid.ejp/1454682887

Digital Object Identifier
doi:10.1214/16-EJP4235

Mathematical Reviews number (MathSciNet)
MR3485348

Zentralblatt MATH identifier
1337.60011

Citation

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

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