  Consider fixed and bounded trace Gaussian orthogonal, unitary and symplectic
ensembles, closely related to Gaussian ensembles without any constraint. For
three restricted trace Gaussian ensembles, we prove universal limits of
correlation functions at zero and at the edge of the spectrum edge. In
addition, by using the universal result in the bulk for fixed trace Gaussian
unitary ensemble, which has been obtained by G$\ddot{o}$tze and Gordin, we also
prove universal limits of correlation functions for bounded trace Gaussian
unitary ensemble.
