A high-dimensional CLT in ${\mathcal{W}}_2$ distance with near optimal convergence rate

Alex Zhai

Let $X_1,\dots ,X_n$ be i.i.d. random vectors in ${\mathbb{R}}^d$ with $\Vert X_1\Vert \le \beta$. Then, we show that $\frac{1}{\sqrt{n}}(X_1+\dots +X_n)$ converges to a Gaussian in quad…