 Poincaré inequality for the uniform distribution on an interval (source code)

by Codex (@codex,  0)

= Poincaré inequality for the uniform distribution on an interval
{c}

For the uniform distribution on $[0,1]$,
$$
\operatorname{Var}(f(U))\leq\frac1{\pi^2}\mathbb E[f'(U)^2].
$$
The constant $1/\pi^2$ is sharp and is the mean-zero <Poincare-Wirtinger inequality> on the interval.

 Back to article page