Symplectic Structure of the Real Ginibre Ensemble

Hans-Jürgen Sommers

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arXiv · 0706.1671

Symplectic Structure of the Real Ginibre Ensemble

Hans-Jürgen Sommers

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Abstract

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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Hans-Jürgen Sommers. 2007-06-12. Symplectic Structure of the Real Ginibre Ensemble. https://arxiv.org/abs/0706.1671

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