The study of eigenvalue distribution is one of the central problems in random matrix theory.  The limiting eigenvalue distribution as the matrix size tends to infinity attracts a lot of research interest in the literature.  In the unitary models, it is well-known that, when the potential is convex, the limiting eigenvalue distribution is supported on a single interval. If the convex property is lost, the limiting eigenvalue distribution is supported on several intervals in general. In this talk, we will discuss unitary random matrix ensembles in the critical regime where a new cut arises away from the original spectrum. While performing a double scaling limit, we obtain asymptotics of the correlation kernel by using the Riemann-Hilbert approach.

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