Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591097 | Journal of Functional Analysis | 2010 | 42 Pages |
Abstract
We prove that for a finite collection of real-valued functions f1,…,fn on the group of complex numbers of modulus 1 which are derivable with Lipschitz continuous derivative, the distribution of under the properly scaled heat kernel measure at a given time on the unitary group U(N) has Gaussian fluctuations as N tends to infinity, with a covariance for which we give a formula and which is of order N−1. In the limit where the time tends to infinity, we prove that this covariance converges to that obtained by P. Diaconis and S.N. Evans in a previous work on uniformly distributed unitary matrices. Finally, we discuss some combinatorial aspects of our results.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory