  We study unitary random matrix ensembles in the critical regime where a new
cut arises away from the original spectrum. We perform a double scaling limit
where the size of the matrices tends to infinity, but in such a way that only a
bounded number of eigenvalues is expected in the newborn cut. It turns out that
limits of the eigenvalue correlation kernel are given by Hermite kernels
corresponding to a finite size Gaussian Unitary Ensemble (GUE). When modifying
the double scaling limit slightly, we observe a remarkable transition each time
the new cut picks up an additional eigenvalue, leading to a limiting kernel
interpolating between GUE-kernels for matrices of size k and size k+1. We prove
our results using the Riemann-Hilbert approach.
