Fermionic Mapping For Eigenvalue Correlation Functions Of (Weakly) Non-Hermitian Symplectic Ensemble

Abstract

The eigenvalues of an arbitrary quaternionic matrix have a joint probability distribution function first derived by Ginibre. We show that there exists a mapping of this system onto a fermionic field theory and then use this mapping to integrate over the positions of the eigenvalues and obtain eigenvalue density as well as all higher correlation functions for both the strongly and weakly non-Hermitian cases.

12 pages, 1 figure, corrected typos. Final published version

References in corpus (1)

• Almost-Hermitian Random Matrices: Eigenvalue Density in the Complex Plane

Cited by in corpus (7)

• Random Matrices close to Hermitian or unitary: overview of methods and results
• Eigenvalue correlations in non-Hermitean symplectic random matrices
• The Complex Laguerre Symplectic Ensemble of Non-Hermitian Matrices
• Critical statistics for non-Hermitian matrices
• Universal eigenvector correlations in quaternionic Ginibre ensembles
• Pfaffian structure of the eigenvector overlap for the symplectic Ginibre ensemble
• Truncations of random symplectic unitary matrices