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?



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.