{"paper":{"title":"On the distribution of maximum value of the characteristic polynomial of GUE random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Nicholas J. Simm, Yan V. Fyodorov","submitted_at":"2015-03-24T17:01:38Z","abstract_excerpt":"Motivated by recently discovered relations between logarithmically correlated Gaussian processes and characteristic polynomials of large random $N \\times N$ matrices $H$ from the Gaussian Unitary Ensemble (GUE), we consider the problem of characterising the distribution of the global maximum of $D_{N}(x):=-\\log|\\det(xI-H)|$ as $N \\to \\infty$ and $x\\in (-1,1)$. We arrive at an explicit expression for the asymptotic probability density of the (appropriately shifted) maximum by combining the rigorous Fisher-Hartwig asymptotics due to Krasovsky \\cite{K07} with the heuristic {\\it freezing transitio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07110","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"}