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We investigate $\beta$-Generalized random Hermitian matrices ensemblesometimes called Chiral ensemble. We give global asymptotic of the density ofeigenvalues or the statistical density. We investigate general method names asequilibrium measure method. When taking $n$ large limit we will see that theasymptotic density of eigenvalues generalize the Wigner semi-circle law.

Generalized $\beta$-Gaussian Ensemble Equilibrium measure method