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

Benoit Collins

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

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arxiv math/0406560 v1 pith:4VNUMSH5 submitted 2004-06-28 math.PR math-phmath.MP

Benoit Collins This is my paper · ORCID

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keywords freejacobipointprobabilityproductpropertiesarisingasymptotics

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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.

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