{"paper":{"title":"Spectral distribution of the free Jacobi process, revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","math.SP"],"primary_cat":"math.PR","authors_text":"Tarek Hamdi","submitted_at":"2017-11-20T15:40:01Z","abstract_excerpt":"We obtain a description for the spectral distribution of the free Jacobi process for any initial pair of projections. This result relies on a study of the unitary operator $RU_tSU_t^*$ where $R,S$ are two symmetries and $U_t$ a free unitary Brownian motion, freely independent from $\\{R,S\\}$. In particular, for non-null traces of $R$ and $S$, we prove that the spectral measure of $RU_tSU_t^*$ possesses two atoms at $\\pm1$ and an $L^\\infty$-density on the unit circle $\\mathbb{T}$, for every $t>0$. Next, via a Szeg\\H{o} type transform of this law, we obtain a full description of the spectral dist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07382","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"}