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

@article{Collins2005ProductOR,
title={Product of random projections, Jacobi ensembles and universality problems arising from free probability},
author={B. Collins},
journal={Probability Theory and Related Fields},
year={2005},
volume={133},
pages={315-344}
}
• B. Collins
• Published 2005
• Mathematics, Physics
• Probability Theory and Related Fields
• Abstract.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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