Second Wasserstein distance
= Second Wasserstein distance
{title2=$W_2(\mu,\nu)$}
For probability measures with finite second moments on a metric space,
$$
W_2(\mu,\nu)^2=\inf\{\mathbb E[\rho(X,Y)^2]:(X,Y)\text{ couples }\mu,\nu\}.
$$
= Second Wasserstein distance
{title2=$W_2(\mu,\nu)$}
For probability measures with finite second moments on a metric space,
$$
W_2(\mu,\nu)^2=\inf\{\mathbb E[\rho(X,Y)^2]:(X,Y)\text{ couples }\mu,\nu\}.
$$