Symplectic Structure of the Real Ginibre Ensemble

Details Symplectic Structure of the Real Ginibre Ensemble Symplectic Structure of the Real Ginibre Ensemble

2007-06-12

arxiv.org/abs/0706.1671v1

Physics

Condensed Matter

Statistical Mechanics

Latex, 7 pages

Scientific paper

We give a simple derivation of all $n$-point densities for the eigenvalues of
the real Ginibre ensemble with even dimension $N$ as quaternion determinants. A
very simple symplectic kernel governs both, the real and complex correlations.
1-and-2-point correlations are discussed in more detail. Scaling forms for
large dimension $N$ are derived.

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