Novel universal correlations in invariant random-matrix models

We show that eigenvalue correlations in unitary-invariant ensembles of large random matrices adhere to 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 genuine density of states and n-point correlation function are completely determined by the Dyson's density analytically continued onto the whole real axis.