{"paper":{"title":"General position of a projection and its image under a free unitary Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Nizar Demni, Taoufik Hmidi","submitted_at":"2013-02-20T09:19:38Z","abstract_excerpt":"Given an orthogonal projection $P$ and a free unitary Brownian motion $Y = (Y_t)_{t \\geq 0}$ in a $W^{\\star}$-non commutative probability space such that $Y$ and $P$ are $\\star$-free in Voiculescu's sense, the main result of this paper states that $P$ and $Y_tPY_t^{\\star}$ are in general position at any time $t$. To this end, we study the dynamics of the unitary operator $SY_tSY_t^{\\star}$ where $S = 2P-1$. More precisely, we derive a partial differential equation for the Herglotz transform of its spectral distribution, say $\\mu_t$. Then, we provide a flow on the interval $[-1,1]$ in such a wa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4844","kind":"arxiv","version":2},"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"}