General Eigenvalue Correlations for the Real Ginibre Ensemble

Details General Eigenvalue Correlations for the Real Ginibre Ensemble General Eigenvalue Correlations for the Real Ginibre Ensemble

2008-06-17

arxiv.org/abs/0806.2756v1

Physics

Condensed Matter

Statistical Mechanics

25 pages, 7 figures

Scientific paper

10.1088/1751-8113/41/40/405003

We rederive in a simplified version the Lehmann-Sommers eigenvalue distribution for the Gaussian ensemble of asymmetric real matrices, invariant under real orthogonal transformations, as a basis for a detailed derivation of a Pfaffian generating functional for $n$-point densities. This produces a simple free-fermion diagram expansion for the correlations leading to quaternion determinants in each order n. All will explicitly be given with the help of a very simple symplectic kernel for even dimension $N$. The kernel is valid both for complex and real eigenvalues and describes a deep connection between both. A slight modification by an artificial additional Grassmannian solves also the more complicated odd-$N$ case. As illustration we present some numerical results in the space $\mathbb{C}^n$ of complex eigenvalue $n$-tuples.

Affiliated with

Also associated with

No associations

Rating

General Eigenvalue Correlations for the Real Ginibre Ensemble does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with General Eigenvalue Correlations for the Real Ginibre Ensemble, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and General Eigenvalue Correlations for the Real Ginibre Ensemble will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-408432