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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 ...

I need to find an exponential bound for $P(|S_n - \mu| > \lambda)$ where $S_n = \frac{1}{D} \sum_{i=1}^D w_i \sin w_iz$ for a constant $z$, $E(S_n) = \mu$ and $w_i$ are drawn from the normal ...

A random variable $X$ is said to be sub-gaussian with mean $\mu$ and pseudo-variance $\sigma^2$ iff $$\mathbb \log(E[\exp(t(X-\mu))]) \le \frac{t^2}{2\sigma^2},\;\forall t \in \mathbb R. $$ It's a ...