5 problems

For a convex symmetric set $K\subset\mathbb{R}^n$, define its inradius by … Let $\gamma_n$ denote standard Gaussian measure on $\mathbb{R}^n$. Vershynin's large-width conjecture. F…

Let $U_1,\dots,U_n$ be independent random variables uniformly distributed on $[-1,1]$, let $a=(a_1,\dots,a_n)$ range over unit vectors in $\mathbb{R}^n$, and let $t>0$. V. Milman's…

Let $d$ and $R$ be fixed, and set $s:=\lfloor R\rfloor+1$. For Bernoulli random variables, let $p(d,R,\operatorname{Ber},n)$ denote the maximal probability that the associated sum…

Let $\operatorname{\mathcal{X}}_{2}^*$ be the set of real random variables of the form … where $c\in\mathbb{R}$, $\beta\in l_2(\mathbb{N})$, $\alpha\in l^2(\mathbb{N})$, and…

For $1\le p<\infty$ and $d\ge2$, let $N(\epsilon,p,d)$ denote the least number of $L^\infty$-balls of radius $\epsilon$ in $C([0,1]^d)$ needed to cover the unit ball of functions o…