Local tail bounds for functions of independent random variables ## AbstractIt 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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