{"paper":{"title":"Truncations of Haar distributed matrices, traces and bivariate Brownian bridges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alain Rouault (LM-Versailles), Catherine Donati-Martin (LPMA)","submitted_at":"2010-07-08T13:11:46Z","abstract_excerpt":"Let U be a Haar distributed unitary matrix in U(n)or O(n). We show that after centering the double index process $$ W^{(n)} (s,t) = \\sum_{i \\leq \\lfloor ns \\rfloor, j \\leq \\lfloor nt\\rfloor} |U_{ij}|^2 $$ converges in distribution to the bivariate tied-down Brownian bridge. The proof relies on the notion of second order freeness."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1366","kind":"arxiv","version":4},"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"}