MathOverflow

I will use the same notation and definitions in High Dimensional Probability, by Roman Vershynin.
I have a sub-Gaussian vector $y$, in $\mathbb{R}^n$ and sub-Gaussian norm $C$ non dependent on $n$. I also assume that $y$ respects the concentration of the norm property, which I define as...

Let\begin{equation*}\Gamma(z)=\int_0^{\infty}t^{z-1}\textrm{e}^{-t}\textrm{d}t, \quad \Re(z)>0\end{equation*}and$$\psi(z)=[\ln\Gamma(z)]'=\frac{\Gamma'(z)}{\Gamma(z)}.$$In the literature, these two functions are respectively called the Euler gamma...

I am looking to build some intuition for a project that I am working on, and I would like to get my hands on interesting concrete examples of finite locally free affine groupoids. For the algebraically inclined, these are anti-equivalent to commutative...

Let $\mathcal{F}$ be an union-closed family of subsets of $[n]=\{1,2,...,n\}$, assume $\varnothing\in\mathcal{F}$. Let $l_i=|\{S|S\in\mathcal{F},i\notin S\}|,u_i=|\{S|S\in\mathcal{F},i\in S\}|$, then $l_i+u_i=|\mathcal{F}|,\forall i\in[n]$. For a set...