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A shorter proof of Kanter's Bessel function concentration bound

Lutz Mattner·Bero Roos
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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 $I_0(x)+I_1(x)$, 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).

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Lutz Mattner, Bero Roos. 2006-10-23. A shorter proof of Kanter's Bessel function concentration bound. https://arxiv.org/abs/math/0603522

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