Large deviations for functions of two random projection matrices
Operator Algebras
2007-05-23 v1 Probability
Abstract
In this paper two independent and unitarily invariant projection matrices P(N) and Q(N) are considered and the large deviation is proven for the eigenvalue density of all polynomials of them as the matrix size converges to infinity. The result is formulated on the tracial state space of the universal -algebra generated by two selfadjoint projections. The random pair determines a random tracial state and satisfies the large deviation. The rate function is in close connection with Voiculescu's free entropy defined for pairs of projections.
Keywords
Cite
@article{arxiv.math/0504435,
title = {Large deviations for functions of two random projection matrices},
author = {F. Hiai and D. Petz},
journal= {arXiv preprint arXiv:math/0504435},
year = {2007}
}
Comments
22 pages