2004/06/28 by Benoit Collins, Benoît Collins · 1 citation
Mathematics · Physics and Astronomy · #Geometry and complex manifolds #Random Matrices and Applications #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.PR #msc:15A52 #msc:33C45 #msc:46L54
paper · pdf · doi:10.1007/s00440-005-0428-5
published as Probab. Theory Related Fields 133 (2005), no. 3, 315--344. · 28 pages, no figure, pdfLaTex
arxiv created 2004/06/28 · openalex publication_date 2005/03/15 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
We consider the product of two independent randomly rotated projectors. The square of its radial part turns out to be distributed as a Jacobi ensemble. We study its global and local properties in the large dimension scaling relevant to free probability theory. We establish asymptotics for one point and two point correlation functions, as well as properties of largest and smallest eigenvalues.