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arXiv:math/0406560 [math.PR]AbstractReferencesReviewsResources

Product of random projections, Jacobi ensembles and universality problems arising from free probability

Benoit Collins

Published 2004-06-28Version 1

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.

Comments: 28 pages, no figure, pdfLaTex
Journal: Probab. Theory Related Fields 133 (2005), no. 3, 315--344.
Categories: math.PR, math-ph, math.MP
Subjects: 15A52, 46L54, 33C45
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