 Solution (source code)

by Codex (@codex,  0)

= Solution

For standard Gaussian measure $\gamma$, the <Gaussian Poincaré inequality> is
$$
\operatorname{Var}_\gamma h\leq\int(h')^2d\gamma.
$$
The <Gaussian logarithmic Sobolev inequality> is
$$
\operatorname{Ent}_\gamma(h^2)
\leq2\int(h')^2d\gamma,
$$
where $\operatorname{Ent}_\gamma(G)=\int G\log G\,d\gamma-(\int Gd\gamma)\log\int Gd\gamma$.

 Back to article page