{"paper":{"title":"Spectral density of complex eigenvalues and associated mean eigenvector self-overlaps at the edge of elliptic Ginibre ensembles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Mark J. Crumpton, Tim R. W\\\"urfel","submitted_at":"2024-05-03T13:58:07Z","abstract_excerpt":"We consider the density of complex eigenvalues, $\\rho(z)$, and the associated mean eigenvector self-overlaps, $\\mathcal{O}(z)$, at the spectral edge of $N \\times N$ real and complex elliptic Ginibre matrices, as $N \\to \\infty$. Two different regimes of ellipticity are studied: strong non-Hermiticity, keeping the ellipticity parameter $\\tau$ fixed and weak non-Hermiticity with $\\tau \\rightarrow 1 $ as $N \\rightarrow \\infty$. At strong non-Hermiticity, we find that both $\\rho(z)$ and $\\mathcal{O}(z)$ have the same leading order behaviour across the elliptic Ginibre ensembles, establishing the ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.02103","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.02103/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}