How to generate random matrices from the classical compact groups

Details How to generate random matrices from the classical compact groups How to generate random matrices from the classical compact groups

2006-09-18

arxiv.org/abs/math-ph/0609050v2

NOTICES of the AMS, Vol. 54 (2007), 592-604

Physics

Mathematical Physics

25 pages, 5 figures, corrected typos

Scientific paper

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.

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