Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Suppose $U$ and $V$ are $n \times n$ random unitary matrices, chosen independently from the Haar measure. Is there any kind of concentration inequality which would be applicable to polynomials $p(U,V)$ in entries of $U$ and $V$? More specifically, I am interested in polynomials of the form:

$ \sum U_{ij}V_{i'j'} X_{ii'}Y_{jj'}$


$ |\sum U_{ij}V_{i'j'} X_{ii'}Y_{jj'}|^2$

where $X$ and $Y$ are some arbitrary matrices and the sum is over all indices. For matrices with i.i.d. Gaussian entries there are well-known concentration bounds for this kind of expressions, I would like to know if there is anything similar for unitary matrices (for this case or for $U=V$).

share|improve this question
For some ideas, please see the comments and answer to my related question: mathoverflow.net/questions/80145/… –  Suvrit May 20 '12 at 0:14

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.