{"paper":{"title":"Spectral properties of non-Hermitian real random matrices with long-range correlations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.PR"],"primary_cat":"cond-mat.dis-nn","authors_text":"Ulysse Marquis","submitted_at":"2026-05-25T11:44:47Z","abstract_excerpt":"We investigate the spectral properties of non-Hermitian real random matrices whose entries exhibit long-range correlations decaying as~$|r-r'|^{-\\alpha}$. We find a progressive breakdown of the circular law, controlled by the decrease of~$\\alpha$. In all cases, the radial eigenvalue density decreases away from the origin. At~$\\alpha>1$, an effective radius, reminiscent of the circular law, is retrieved, while instead, for~$\\alpha<1$, the eigenvalue distribution broadens with matrix size and its spectral radius grows like a power law, with exponents numerically close to the exponents controllin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25736","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.25736/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"}