Averages of Spectral Determinants and `Single Ring Theorem' of Feinberg and Zee
Abstract
We compute < det (Iz-H) (Iz-H)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 HHdagger . Under the assumption that 1 over N ln < det (Iz-H) (Iz-H)dagger rangle H is asymptotically equal to 1over N < ln det (Iz-H) (Iz-H)dagger rangle H we reproduce the eigenvalue distribution of H obtained previously by Feinberg and Zee, Nucl. Phys. B501, 643 (1997).
- Publication:
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Acta Physica Polonica B
- Pub Date:
- December 2007
- Bibcode:
- 2007AcPPB..38.4067F