{"paper":{"title":"On the distribution of the largest real eigenvalue for the real Ginibre ensemble","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"M. Poplavskyi, Oleg Zaboronski, Roger Tribe","submitted_at":"2016-03-18T11:41:20Z","abstract_excerpt":"Let $\\sqrt{N}+\\lambda_{max}$ be the largest real eigenvalue of a random $N\\times N$ matrix with independent $N(0,1)$ entries (the `real Ginibre matrix'). We study the large deviations behaviour of the limiting $N\\rightarrow \\infty$ distribution $P[\\lambda_{max}<t]$ of the shifted maximal real eigenvalue $\\lambda_{max}$. In particular, we prove that the right tail of this distribution is Gaussian: for $t>0$, \\[ P[\\lambda_{max}<t]=1-\\frac{1}{4}\\mbox{erfc}(t)+O\\left(e^{-2t^2}\\right). \\] This is a rigorous confirmation of the corresponding result of Forrester and Nagao. We also prove that the left"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05849","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":""},"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"}