A Classification of Non-Hermitian Random Matrices
Disordered Systems and Neural Networks
2020-02-27 v2 Statistical Mechanics
Abstract
We present a classification of non-hermitian random matrices based on implementing commuting discrete symmetries. It contains 38 classes. This generalizes the classification of hermitian random matrices due to Altland-Zirnbauer and it also extends the Ginibre ensembles of non-hermitian matrices.
Keywords
Cite
@article{arxiv.cond-mat/0110649,
title = {A Classification of Non-Hermitian Random Matrices},
author = {Denis Bernard and Andre LeClair},
journal= {arXiv preprint arXiv:cond-mat/0110649},
year = {2020}
}
Comments
8 pages, contribution to the proceedings of the NATO Advanced Research Workshop on Statistical Field Theories, Como (Italy), 18-23 June 2001. Compared to our 2001 version, we corrected two misprints in one table that in the previous version led us to miscount the number of classes as 43 whereas it should have been 38. Explicit details of the classification are unchanged