Novel Universal Correlations in Invariant Random-Matrix Models

We show that eigenvalue correlations in unitary-invariant ensembles of large random matrices satisfy novel universal laws that only depend on a multicriticality of the bulk density of states near the soft edge of the spectrum. Our consideration is based on the previously unknown observation that the genuine density of states and the $n$-point correlation function are completely determined by the Dyson's density analytically continued onto the entire real axis.