Beta Jacobi Ensembles and Associated Jacobi Polynomials

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