A correlation inequality for random points in a hypercube with some implications

Royi Jacobovic, Or Zuk

Let $\prec$ be the product order on ${\mathbb{R}}^k$ and assume that $X_1,X_2,\dots ,X_n$ ($n\ge 3$) are i.i.d. random vectors distributed uniformly in the unit hypercube $[0,1{]}^k$.…