Averages of Spectral Determinants and `Single Ring Theorem' of Feinberg and Zee
Abstract
We compute < det (IzH) (IzH)^{dagger } rangle _{H} in the limit of infinite matrix dimension N for complex random matrices H with invariant matrix distribution in terms of the eigenvalue distribution of the Hermitian random matrices HH^{dagger }. Under the assumption that 1 over N ln < det (IzH) (IzH)^{dagger } rangle _{H} is asymptotically equal to 1over N < ln det (IzH) (IzH)^{dagger } rangle _{H} we reproduce the eigenvalue distribution of H obtained previously by Feinberg and Zee, Nucl. Phys. B501, 643 (1997).
 Publication:

Acta Physica Polonica B
 Pub Date:
 December 2007
 Bibcode:
 2007AcPPB..38.4067F