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

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

2004-06-28

arxiv.org/abs/math/0406560v1

Probab. Theory Related Fields 133 (2005), no. 3, 315--344.

Mathematics

Probability

28 pages, no figure, pdfLaTex

Scientific paper

10.1007/s00440-005-0428-5

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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