All Questions

The following problem has a beautiful geometric interpretation in terms of the proportion of points on the Euclidean sphere in $\mathbb{R}^d$ that lie at least a certain distance away from a $k$-...

I have been working on a problem(alternate minimization) where I want to establish an inequality in which I am stuck. An $\alpha$- parameterized version of the divergence(Kullback-Leibler) takes the ...

Let $S_n$ be a set of $n$ points belonging to $\mathcal{B}_d:=\{\mathbf{x}\in\mathbb{R}^d:\|\mathbf{x}\|_2\le 1\}$, where $d\ll \log(n)$. Let $s_n$ and $\ell_n$ be respectively defined as follows: $$...

Let $x \le y \le z$ be the length of the sides of a triangle whose vertices are uniformly random on the circumference of a circle. In this question, it was proved that if $a \ge 1$, then the ...