The Riemann-Hilbert approach to double scaling limit of random matrix eigenvalues near the ”birth of a cut” transition
نویسنده
چکیده
In this paper we studied the double scaling limit of a random unitary matrix ensemble near a singular point where a new cut is emerging from the support of the equilibrium measure. We obtained the asymptotic of the correlation kernel by using the Riemann-Hilbert approach. We have shown that the kernel near the critical point is given by the correlation kernel of a random unitary matrix ensemble with weight e −x2ν . This provides a rigorous proof of the previous results in [18].
منابع مشابه
The birth of a cut in unitary random matrix ensembles
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 correspond...
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