The Riemann-Hilbert approach to double scaling limit of random matrix eigenvalues near the "birth of a cut" transition

Details The Riemann-Hilbert approach to double scaling limit of random matrix eigenvalues near the "birth of a cut" transition The Riemann-Hilbert approach to double scaling limit of random matrix eigenvalues near the "birth of a cut" transition

2007-11-21

arxiv.org/abs/0711.3208v1

Physics

Mathematical Physics

41 pages, 3 figures

Scientific paper

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 $e^{-x^{2\nu}}$. This provides a rigorous proof of the previous results of Eynard.

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