Jiao-Xue Wang

Sharp Fourth-Moment Wasserstein CLT Bounds

We prove that for the normalized sum $W=\sum_{i=1}^n X_i/\sqrt{n}$ of independent, mean-zero, $d$-dimensional random vectors with $\operatorname{Cov}(W) =\Sigma=\operatorname{diag}(\sigma_1^2,\dots, \sigma_d^2)$ (the diagonal form of the covariance matrix is assumed without loss of generality), the 2-Wasserstein distan...