The Sylvester question in ${\mathbb{R}}^d$: convex sets with a flat floor

Jean-François Marckert, Ludovic Morin

Pick $n$ independent and uniform random points $U_1,\dots ,U_n$ in a compact convex set $K$ of ${\mathbb{R}}^d$ with volume 1, and let $P_K^{(d)}(n)$ be the probability that these po…