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Minimum separation among $m$ random points on an $n$-dimensional unit sphere
Consider $m$ points $v_1, \ldots, v_m \in R^{n}$, which are uniformly distributed on the $n$-dimensional unit sphere $S^{n-1} = \{v:\|v\|_2 = 1\}$. Let the minimum separation be
$$
\rho = \min_{i,j\in{...
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Integral of product of Hermite polynomials w.r.t marginal distribution of first two-coordinate of random vector on unit-sphere
This question is related to: https://math.stackexchange.com/q/4270522/168758
Let $H_n(x) \in \mathbb R[x]$ be the probabilist's $n$th Hermite polynomial. This an $n$th degree polynomial given by the ...
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2
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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 ...
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