  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.
