EFFECTIVE-FIELD APPROACH TO THE GAUSSIAN RANDOM-MATRIX MODEL

A Hermitian random-matrix model with an arbitrary Gaussian distributio n of the matrix elements is proposed and studied by means of effective -field theory. We construct an effective action as a functional of the eigenvalue distribution. Using this effective action, we obtain the e ntire N-level distribution function in the mean-field approximation. W e show a smooth transition from the Gaussian Unitary Ensemble to the P oisson level distribution in the same delocalized phase. The connectio n to previous results is discussed.