Abstract
We present a classification of non-Hermitian random matrices based on implementing commuting discrete symmetries. It contains 43 classes. This generalizes the classification of Hermitian random matrices due to Altland-Zirnbauer and it also extends the Ginibre ensembles of non-Hermitian matrices.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
F. Dyson, J. Math. Phys. 3 (1962) 140.
M. Mehta, Random matrices, Academic Press, Boston, 1991.
A. Altland and M. Zirnbauer, Phys. Rev. B 55 (1997) 1142; M. Zirnbauer, J. Math. Phys. 37 (1996) 4986.
J. Ginibre, J. Math. Phys. 6 (1965) 440.
Y.V. Fyodorov and H.J. Sommers, J. Math. Phys. 38 (1997) 1918, and references therein.
M. Bauer, D. Bernard and J.-M. Luck, J. Phys. A 34 (2001) 2659.
D. Bernard and A. LeClair, “A classification of 2d random Dirac fermions”, preprint cond-mat/0109552.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Bernard, D., LeClair, A. (2002). A Classification of Non-Hermitian Random Matrices. In: Cappelli, A., Mussardo, G. (eds) Statistical Field Theories. NATO Science Series, vol 73. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0514-2_19
Download citation
DOI: https://doi.org/10.1007/978-94-010-0514-2_19
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-0761-3
Online ISBN: 978-94-010-0514-2
eBook Packages: Springer Book Archive