{"paper":{"title":"A unitary extension of virtual permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. Nikeghbali, J. Najnudel, P. Bourgade","submitted_at":"2011-02-13T19:59:31Z","abstract_excerpt":"Analogously to the space of virtual permutations, we define projective limits of isometries: these sequences of unitary operators are natural in the sense that they minimize the rank norm between successive matrices of increasing sizes. The space of virtual isometries we construct this way may be viewed as a natural extension of the space of virtual permutations of Kerov, Olshanski and Vershik as well as the space of virtual isometries of Neretin. We then derive with purely probabilistic methods an almost sure convergence for these random matrices under the Haar measure: for a coherent Haar me"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2633","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"}