Looking for a reference on what I think is a standard result.
For a measure $\mu \in P(\mathbb{R}^n)$, let $y_1, \dots, y_N \sim \mu$ be independent samples.
The empirical distribution associated with the samples is the discrete measure $$ \hat{\mu} = \frac{1}{N} \sum_{i=1}^N \delta_{Y_i} \,.$$
Can we bound the Wasserstein distance $W_2(\mu,\hat{\mu})$?
I heard somewhere that it is of order $\frac{1}{\sqrt{N}}$ with high probability, but I can't find a reference.