Rate of convergence of linear functions on the unitary group

Details Rate of convergence of linear functions on the unitary group Rate of convergence of linear functions on the unitary group

2010-09-03

arxiv.org/abs/1009.0695v2

J. Phys. A: Math. Theor., Vol. 44 (2011), 035204

Physics

Mathematical Physics

34 pages, 1 figure; corrected typos, added remark 3.3, added 3 references

Scientific paper

We study the rate of convergence to a normal random variable of the real and imaginary parts of Tr(AU), where U is an N x N random unitary matrix and A is a deterministic complex matrix. We show that the rate of convergence is O(N^{-2 + b}), with 0 <= b < 1, depending only on the asymptotic behaviour of the singular values of A; for example, if the singular values are non-degenerate, different from zero and O(1) as N -> infinity, then b=0. The proof uses a Berry-Esse'en inequality for linear combinations of eigenvalues of random unitary, matrices, and so appropriate for strongly dependent random variables.

Affiliated with

Also associated with

No associations

Rating

Rate of convergence of linear functions on the unitary group does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Rate of convergence of linear functions on the unitary group, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rate of convergence of linear functions on the unitary group will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-685039