A shorter proof of Kanter's Bessel function concentration bound

2006/03/21 by Mattner, Lutz, Roos, Bero
#33C10 #60E15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.math/0603522

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), 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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