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We consider $\beta$-Jacobi ensembles with parameters $p_1, p_2\geq n.$ Weprove that the empirical measure of the rescaled Jacobi ensembles convergesweakly to a modified Watcher law via the spectral measure method, whichrevisits the weak limits obtained in \cite{MaLDPJ} while replacing thecondition $\beta n\!>\!> \log n$ by $\beta n\!>\!>1.$  We also provide the central limit theorem and the large deviation for thecorresponding rescaled spectral measure.

Nonstandard limit theorems and large deviation for beta -Jacobi ensembles with a different scaling