All Questions

The Carbery–Wright inequality is a seminal result about the anti-concentration of polynomials of Gaussian random variables. See e.g. Meka, Nguyen, and Vu - Anti-concentration for polynomials of ...

Suppose $X \sim N(0, \Sigma)$ is a $d$-dimensional Gaussian random vector. And we have $2n$ $i.i.d$ sample $X_1, \ldots, X_{n}, \ldots, X_{2n}$. Let $\hat{\Sigma}_1 = \frac{1}{n}\sum_{i=1}^nX_i X_i^\...

This might be a too easy question for Mathoverflow, but Googling led to similar questions and answers here (though not the one I was looking for). The question is split into two: I have a matrix $X \...

Let $\mathbf{1}\in\mathbb{R}^d$ be the $d$-dimensional all-ones vector and let $n\sim\mathcal{N}(0, \sigma^2 I_{d\times d})$, show that $$ \frac{\| \mathbf{1} + n \|_1}{\|\mathbf{1} + n \|_2} \ge c \...