{"paper":{"title":"Bridges and random truncations of random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alain Rouault, Catherine Donati-Martin, Vincent Beffara","submitted_at":"2013-12-09T11:12:23Z","abstract_excerpt":"We continue to study the squared Frobenius norm of a submatrix of a $n \\times n$ random unitary matrix. When the choice of the submatrix is deterministic and its size is $[ns] \\times [nt]$, we proved in a previous paper that, after centering and without any rescaling, the two-parameter process converges in distribution to a bivariate Brownian bridge. Here, we consider Bernoulli independent choices of rows and columns with respective parameters $s$ and $t$. We prove by subordination that after centering and rescaling by $n^{-1/2}$, the process converges to another Gaussian process."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2382","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":""},"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"}