Steinhaus random variable
= Steinhaus random variable
{c}
{title2=$\eta=e^{i\Theta},\quad\Theta\sim\operatorname{Unif}[0,2\pi)$}
A Steinhaus random variable is uniformly distributed on the complex unit circle. It can be generated as $\epsilon\cos\theta+i\delta\sin\theta$ using independent signs $\epsilon,\delta$ and an independent uniform angle $\theta\in[0,\pi/2]$. This conditional sign representation transfers <Rademacher sum> inequalities to random complex phases.