{"paper":{"title":"Liberation of Projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CV","math.OA","math.PR"],"primary_cat":"math.FA","authors_text":"Benoit Collins, Todd Kemp","submitted_at":"2012-11-26T17:49:28Z","abstract_excerpt":"We study the liberation process for projections: $(p,q)\\mapsto (p_t,q)= (u_tpu_t^\\ast,q)$ where $u_t$ is a free unitary Brownian motion freely independent from $\\{p,q\\}$. Its action on the operator-valued angle $qp_tq$ between the projections induces a flow on the corresponding spectral measures $\\mu_t$; we prove that the Cauchy transform of the measure satisfies a holomorphic PDE. We develop a theory of subordination for the boundary values of this PDE, and use it to show that the spectral measure $\\mu_t$ possesses a piecewise analytic density for any $t>0$ and any initial projections of trac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6037","kind":"arxiv","version":3},"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"}