English

A shorter proof of Kanter's Bessel function concentration bound

Probability 2007-05-23 v2 Classical Analysis and ODEs

Abstract

We give a shorter proof of Kanter's (1976) sharp Bessel function bound for concentrations of sums of independent symmetric random vectors. We provide sharp upper bounds for the sum of modified Bessel functions I0(x)+I1(x)I_0(x)+I_1(x), which might be of independent interest. Corollaries improve concentration or smoothness bounds for sums of independent random variables due to Cekanavicius & Roos (2006), Roos (2005), Barbour & Xia 1999), and Le Cam (1986).

Keywords

Cite

@article{arxiv.math/0603522,
  title  = {A shorter proof of Kanter's Bessel function concentration bound},
  author = {Lutz Mattner and Bero Roos},
  journal= {arXiv preprint arXiv:math/0603522},
  year   = {2007}
}

Comments

12 pages. Two references added. Accepted for publication by Probability Theory and Related Fields