Talagrand's one-sided bounded differences inequality
= Talagrand's one-sided bounded differences inequality
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If a function of independent coordinates has one-sided squared-difference proxy at most $v$, Talagrand's one-sided inequality gives a Gaussian lower-tail bound $\mathbb P(Z-\mathbb EZ\leq-t)\leq e^{-t^2/(2v)}$. Applied to the negative of a concave function, it gives the corresponding upper-tail bound.