All Questions

Let $(a_k)_{k \geq 1}$ be random variables taking values on a finite subset $B$. Assume that $$ (1) \quad \Pr\Big (\lim_{n\rightarrow +\infty}d(\frac{1}{n}\sum_{k=1}^n 1_{[a_k = b]}, [v_\ell(b,\...

Consider a convex set, say $S = [0,1]^d$. Let $X_1, X_2,\ldots,X_n, \ldots$ be i.i.d. random variables that are uniformly distributed on $S$. Denote the Euclidean ball centered at $x \in \mathbb{R}^d$ ...

Suppose you have a centrally symmetric convex 2D shape $C$ of area $A$, and you randomly throw down copies of $C$ on the plane so that each $C$-center lies within a given unit square $S$, until $S$ is ...