= Bernstein concentration inequality for products of sub-Gaussian variables
{c}
For <independent random variables>[independent] identically distributed pairs $(U_i,V_i)$ whose coordinates are <sub-Gaussian random variable>[sub-Gaussian] with parameter $\sigma/4$, <Bernstein's inequality> applied to the centered products gives
$$
\mathbb P\!\left(
\left|\frac1n\sum_{i=1}^n\{U_iV_i-\mathbb E(U_iV_i)\}\right|\geq t
\right)
\leq2\exp\!\left(-\frac{2nt^2}{\sigma^2(\sigma^2+t)}\right).
$$
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