{"paper":{"title":"Almost-Hermitian Random Matrices: Eigenvalue Density in the Complex Plane","license":"","headline":"","cross_cats":["chao-dyn","hep-lat","hep-th","nlin.CD"],"primary_cat":"cond-mat","authors_text":"Boris A. Khoruzhenko, Hans-Juergen Sommers, Yan V. Fyodorov","submitted_at":"1996-06-24T13:14:45Z","abstract_excerpt":"We consider an ensemble of large non-Hermitian random matrices of the form $\\hat{H}+i\\hat{A}_s$, where $\\hat{H}$ and $\\hat{A}_s$ are Hermitian statistically independent random $N\\times N$ matrices. We demonstrate the existence of a new nontrivial regime of weak non-Hermiticity characterized by the condition that the average of $N\\mbox{Tr} \\hat{A}_s^2$ is of the same order as that of $\\mbox{Tr} \\hat{H}^2 $ when $N\\to \\infty$. We find explicitly the density of complex eigenvalues for this regime in the limit of infinite matrix dimension. The density determines the eigenvalue distribution in the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9606173","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}