Local tail bounds for functions of independent random variables
Luc Devroye and Gábor Lugosi
Annals of Probability Volume 36, pp. 143-159, 2008.

Abstract

It is shown that functions defined on {0, 1, . . . , r − 1} n satisfying certain condi- tions of bounded differences that guarantee subgaussian tail behavior also satisfy a much stronger “local” subgaussian property. For self-bounding and configuration functions we derive analogous locally subexponential behavior. The key tool is Talagrand’s (1994) vari- ance 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 ≥ 2.

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