1997/03/10 by Joshua Feinberg, J. Feinberg, A. Zee · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Matrix Theory and Algorithms #Quantum Information and Cryptography #Random Matrices and Applications #cond-mat #hep-th
paper · pdf · doi:10.1016/s0550-3213(97)00502-6
published as Nucl.Phys. B504 (1997) 579-608 · 46 pages, 3 ps figures, LaTex
arxiv created 1997/03/10 · openalex publication_date 1997/11/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We consider random non-hermitean matrices in the large N limit. The power of analytic function theory cannot be brought to bear directly to analyze non-hermitean random matrices, in contrast to hermitean random matrices. To overcome this difficulty, we show that associated to each ensemble of non-hermitean matrices there is an auxiliary ensemble of random hermitean matrices which can be analyzed by the usual methods. We then extract the Green's function and the density of eigenvalues of the non-hermitean ensemble from those of the auxiliary ensemble. We apply this "method of hermitization" to several examples, and discuss a number of related issues.