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arXiv · 0712.1686

Local tail bounds for functions of independent random variables

Luc Devroye·Gábor Lugosi
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Abstract

It is shown that functions defined on $\{0,1,...,r-1\}^n$ satisfying certain conditions of bounded differences that guarantee sub-Gaussian tail behavior also satisfy a much stronger ``local'' sub-Gaussian property. For self-bounding and configuration functions we derive analogous locally subexponential behavior. The key tool is Talagrand's [Ann. Probab. 22 (1994) 1576--1587] variance inequality for functions defined on the binary hypercube which we extend to functions of uniformly distributed random variables defined on $\{0,1,...,r-1\}^n$ for $r\ge2$.

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Luc Devroye, Gábor Lugosi. 2007-12-11. Local tail bounds for functions of independent random variables. https://doi.org/10.1214/00911797000000088

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