{"paper":{"title":"Segal-Bargmann transform: the $q$-deformation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.PR","authors_text":"Ching-Wei Ho, Guillaume C\\'ebron","submitted_at":"2017-03-21T18:51:20Z","abstract_excerpt":"We give identifications of the $q$-deformed Segal-Bargmann transform and define the Segal-Bargmann transform on mixed $q$-Gaussian variables. We prove that, when defined on the random matrix model of \\'Sniady for the $q$-Gaussian variable, the classical Segal-Bargmann transform converges to the $q$-deformed Segal-Bargmann transform in the large $N$ limit. We also show that the $q$-deformed Segal-Bargmann transform can be recovered as a limit of a mixture of classical and free Segal-Bargmann transform."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07388","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"}