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In Statistics, there's a standard test of independence of two random variables taking values in finite sets $I,J$. It relies on the computation of $\chi$-square statistics, $$ \chi^2:=\sum_{(i,j)\in ...

The concentration of measure on the cube $ [0, 1]^n $ equipped with uniform probability measure $\mu_{\infty}$, states that for any $A \subset [0, 1]^n $ with $ \mu_{\infty}(A) \geq \frac{1}{2} $, we ...

This question is somewhat related to the question Intersecting cylinders, but where the cylinders are now modified to orbifolds in the hypercube with singularities occurring at the vertices of the ...

Denote the unit $\ell_2$ ball in $\mathbb{R}^n$ as $\mathcal{B}_n$. It is widely kown that for a convex body $\mathcal{K}\subseteq \mathbb{R}^n$, the $n$-dimensional volume of the parallel body $\...