Probability Theory and Related Fields

, Volume 133, Issue 3, pp 315–344 | Cite as

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

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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.

Keywords

Correlation Function Stochastic Process Probability Theory Mathematical Biology Local Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of MathematicsGraduate School of Science Kyoto UniversityKyotoJapan

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