## Products of random projections, Jacobi ensembles and universality problems arising from free probability. Probab. Theory Rel (2005)

Venue: | Fields |

Citations: | 30 - 1 self |

### BibTeX

@ARTICLE{Collins05productsof,

author = {Benoît Collins},

title = {Products of random projections, Jacobi ensembles and universality problems arising from free probability. Probab. Theory Rel},

journal = {Fields},

year = {2005}

}

### OpenURL

### Abstract

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. 1. INTRODUCTION. In this paper, we consider the asymptotic distribution of eigenvalues of a random matrix of the form πn ˜πnπn where πn and ˜πn are independent n×n random orthogonal projections, of ranks qn and ˜qn, whose distributions are invariant under unitary conjugation. This question is part of a more general