# A high-dimensional CLT in $\mathcal {W}_2$ W 2 distance with near optimal convergence rate

Probability Theory and Related Fields, pp. 821-845, 2018.

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Let (X_1,ldots ,X_n) be i.i.d. random vectors in (mathbb {R}^d) with (Vert X_1Vert le beta ). Then, we show that $begin{aligned} frac{1}{sqrt{n}}left( X_1 + cdots + X_nright) end{aligned}$converges to a Gaussian in quadratic transportation (also known as “Kantorovich” or “Wasserstein”) distance at a rate of (O left( frac{sqrt{d} beta lo...More

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