{"paper":{"title":"Asymptotic freeness in tracial ultraproducts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.LO"],"primary_cat":"math.OA","authors_text":"Adrian Ioana, Cyril Houdayer","submitted_at":"2023-09-26T15:58:27Z","abstract_excerpt":"We prove novel asymptotic freeness results in tracial ultraproduct von Neumann algebras. In particular, we show that whenever $M = M_1 \\ast M_2$ is a tracial free product von Neumann algebra and $u_1 \\in \\mathscr U(M_1)$, $u_2 \\in \\mathscr U(M_2)$ are Haar unitaries, the relative commutants $\\{u_1\\}' \\cap M^{\\mathcal U}$ and $\\{u_2\\}' \\cap M^{\\mathcal U}$ are freely independent in the ultraproduct $M^{\\mathcal U}$. Our proof relies on Mei-Ricard's results [MR16] regarding $\\operatorname{L}^p$-boundedness (for all $1 < p < +\\infty$) of certain Fourier multipliers in tracial amalgamated free pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.15029","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.15029/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}