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Answer by Marcus M for $d$-ball approximation for $d\gg 1$ with a convex hull...
It's true deterministically in $P_n$. In fact, here's a proof that there is some $c$ so that if $n \leq e^{cd}$ then we have that $V(C_n)/V(S^d) \to 0$.We'll work with the ball of radius $1$. For a...
View Article$d$-ball approximation for $d\gg 1$ with a convex hull of random points on...
Given a $d$-ball $\mathcal{S}^{d}$, let $P_n$ a set of $n$ points selected uniformly at random on the boundary $\mathcal{S}^{d-1}$ of $\mathcal{S}^{d}$. Let $\mathcal{C}_n$ the convex hull of $P_n$. We...
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