How to generate random matrices from the classical compact groups
Abstract
We discuss how to generate random unitary matrices from the classical compact groups U(N), O(N) and USp(N) with probability distributions given by the respective invariant measures. The algorithm is straightforward to implement using standard linear algebra packages. This approach extends to the Dyson circular ensembles too. This article is based on a lecture given by the author at the summer school on Number Theory and Random Matrix Theory held at the University of Rochester in June 2006. The exposition is addressed to a general mathematical audience.
 Publication:

arXiv eprints
 Pub Date:
 September 2006
 arXiv:
 arXiv:mathph/0609050
 Bibcode:
 2006math.ph...9050M
 Keywords:

 Mathematical Physics;
 Mathematics  Numerical Analysis;
 1502;
 15A52;
 65F25
 EPrint:
 25 pages, 5 figures, corrected typos