Limit correlation functions at zero for fixed trace random matrix ensembles

The large-$N$ limit of the eigenvalue correlation functions is examined in a neighborhood of zero for the spectra of $N\times N-$Hermitian matrices chosen at random from the Hilbert–Schmidt sphere of appropriate radius. Dyson's famous $\sin\pi(t_1-t_2)/\pi(t_1-t_2)$-kernel asymptotics is extended to this class of random matrix ensembles.