Universality for eigenvalue correlations from the modified Jacobi unitary ensemble

Details Universality for eigenvalue correlations from the modified Jacobi unitary ensemble Universality for eigenvalue correlations from the modified Jacobi unitary ensemble

2002-04-02

arxiv.org/abs/math-ph/0204006v1

International Mathematics Research Notices 2002 No 30 (2002), 1575-1600

Physics

Mathematical Physics

19 pages, 3 figures

Scientific paper

The eigenvalue correlations of random matrices from the Jacobi Unitary Ensemble have a known asymptotic behavior as their size tends to infinity. In the bulk of the spectrum the behavior is described in terms of the sine kernel, and at the edge in terms of the Bessel kernel. We will prove that this behavior persists for the Modified Jacobi Unitary Ensemble. This generalization of the Jacobi Unitary Ensemble is associated with the modified Jacobi weight w(x)=(1-x)^\alpha (1+x)^\beta h(x) where the extra factor h is assumed to be real analytic and strictly positive on [-1,1]. We use the connection with the orthogonal polynomials with respect to the modified Jacobi weight, and recent results on strong asymptotics derived by K.T-R McLaughlin, W. Van Assche and the authors.

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