Second Order Freeness and Fluctuations of Random Matrices: II. Unitary Random Matrices

Details Second Order Freeness and Fluctuations of Random Matrices: II. Unitary Random Matrices Second Order Freeness and Fluctuations of Random Matrices: II. Unitary Random Matrices

2004-05-13

arxiv.org/abs/math/0405258v2

Advances in Mathematics, Volume 209, Issue 1, 15 February 2007, Pages 212-240

Mathematics

Operator Algebras

31 pages, new section on failure of universality added, typos corrected, additional explanations

Scientific paper

10.1016/j.aim.2006.05.003

We extend the relation between random matrices and free probability theory from the level of expectations to the level of fluctuations. We show how the concept of "second order freeness", which was introduced in Part I, allows one to understand global fluctuations of Haar distributed unitary random matrices. In particular, independence between the unitary ensemble and another ensemble goes in the large $N$ limit over into asymptotic second order freeness. Two important consequences of our general theory are: (i) we obtain a natural generalization of a theorem of Diaconis and Shahshahani to the case of several independent unitary matrices; (ii) we can show that global fluctuations in unitarily invariant multi-matrix models are not universal.

Affiliated with

Also associated with

No associations

Rating

Second Order Freeness and Fluctuations of Random Matrices: II. Unitary Random Matrices 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 Second Order Freeness and Fluctuations of Random Matrices: II. Unitary Random Matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Second Order Freeness and Fluctuations of Random Matrices: II. Unitary Random Matrices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-618913