Correlation Functions of Asymmetric Real Matrices

Abstract

We give a closed form for the correlation functions of ensembles of asymmetric real matrices in terms of the Pfaffian of an antisymmetric matrix formed from a $2\times 2$ matrix kernel associated to the ensemble. We also derive closed forms for the matrix kernel and correlation functions for Ginibre's real ensemble.

34 pages. This revision contains new content and some corrections

References in corpus (2)

• Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices
• Random Matrices: The circular Law