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Wasserstein distance between $N(0,1/d)$ and the marginal distribution of $x_1$ when $x=(x_1,\ldots,x_d)$ is uniform on the unit-sphere in $R^d$

Let $x=(x_1,\ldots,x_d)$ be uniformly distributed on the unit-sphere in $\mathbb R^d$. Question. What is a good upper-bound for Wasserstein distance between $N(0,1/d)$ and the marginal distribution ...

dohmatob

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asked Aug 10, 2021 at 19:21

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Wasserstein distance between $N(0,1/d)$ and the marginal distribution of $x_1$ when $x=(x_1,\ldots,x_d)$ is uniform on the unit-sphere in $R^d$

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Wasserstein distance between $N(0,1/d)$ and the marginal distribution of $x_1$ when $x=(x_1,\ldots,x_d)$ is uniform on the unit-sphere in $R^d$

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