{"paper":{"title":"Freezing Transitions and Extreme Values: Random Matrix Theory, $\\zeta(1/2+it)$, and Disordered Landscapes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.MP","math.NT","math.PR"],"primary_cat":"math-ph","authors_text":"Jonathan P. Keating, Yan V. Fyodorov","submitted_at":"2012-11-26T18:54:23Z","abstract_excerpt":"We argue that the freezing transition scenario, previously conjectured to occur in the statistical mechanics of 1/f-noise random energy models, governs, after reinterpretation, the value distribution of the maximum of the modulus of the characteristic polynomials p_N(\\theta) of large N\\times N random unitary (CUE) matrices; i.e. the extreme value statistics of p_N(\\theta) when N \\rightarrow\\infty. In addition, we argue that it leads to multifractal-like behaviour in the total length \\mu_N(x) of the intervals in which |p_N(\\theta)|>N^x, x>0, in the same limit. We speculate that our results exte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6063","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"}