  Beta ensembles on the real line with three classical weights (Gaussian,
Laguerre and Jacobi) are now realized as the eigenvalues of certain tridiagonal
random matrices. The paper deals with beta Jacobi ensembles, the type with the
Jacobi weight. Making use of the random matrix model, we show that in the
regime where $\beta N \to const \in [0, \infty)$, with $N$ the system size, the
empirical distribution of the eigenvalues converges weakly to a limiting
measure which belongs to a new class of probability measures of associated
Jacobi polynomials. This is analogous to the existing results for the other two
classical weights. We also study the limiting behavior of the empirical measure
process of beta Jacobi processes in the same regime and obtain a dynamic
version of the above.
