4 problems

Let $\Lambda\subset\mathbb{R}^2$ be a bounded connected set with regular boundary, let…

Let $Q=[0,1]^2$, let $\mu(\mathop{}\!\mathrm{d}{\boldsymbol{x}})=\rho({\boldsymbol{x}})\mathop{}\!\mathrm{d}{\boldsymbol{x}}$ be a probability measure on $Q$ with smooth positive d…

Let $Q=[0,1]^2$, let $\sigma$ be the uniform probability measure on $Q$, and let $X^N$ be the empirical measure of $N$ independent points sampled from $\sigma$. Caracciolo et al.'s…

Let $Q=[0,1]^2$, and let $X^N$ and $Y^N$ be the empirical measures of two independent samples of $N$ points uniformly distributed on $Q$. Equivalently, let $C_N=N W_2^2(X^N,Y^N)$ b…