1
$\begingroup$

I would like find tail bounds for the expression $$ \begin{align*} \left|\left\langle a,\phi\right\rangle \left\langle \phi,b\right\rangle -\left\langle a,b\right\rangle\right|, \end{align*} $$ where $a$ and $b$ are fixed complex vectors and $\phi$ is a vector with iid Rademacher entries. I know that this is a special case of Hanson-Wright inequality, but I couldn't find any reference that explicitly considers complex matrices. I hesitate to derive the desired bound using the real version, because I would like to obtain reasonably sharp constant factors.

Question: Can anyone point me to a reference that directly addresses complex Hanson-Wright inequality, or at least my special case?

$\endgroup$

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.