Large deviations for functions of two random projection matrices

2005/04/21 by Fumio Hiai, F. Hiai, Hiai, F. +2
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Random Matrices and Applications #math.OA #math.PR #msc:15A52 #msc:46L54 #msc:60F10

paper · pdf · doi:10.48550/arxiv.math/0504435

22 pages

arxiv created 2005/04/21 · arxiv updated 2009/12/01

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 N converges to infinity. The result is formulated on the tracial state space TS(\cal A) of the universal C^*-algebra \cal A generated by two selfadjoint projections. The random pair (P(N),Q(N)) determines a random tracial state τ_N ∈ TS(\cal A) and τ_N satisfies the large deviation. The rate function is in close connection with Voiculescu's free entropy defined for pairs of projections.

Citations

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