  Using the Coulomb gas method and standard methods of statistical physics, we
compute analytically the joint cumulative probability distribution of the
extreme eigenvalues of the Jacobi-MANOVA ensemble of random matrices, in the
limit of large matrices. This allows us to derive the rate functions for the
large fluctuations to the left and the right of the expected values of the
smallest and largest eigenvalues analytically. Our findings are compared with
some available known exact results as well as with numerical simulations
finding good agreement.
