The RiemannHilbert approach to double scaling limit of random matrix eigenvalues near the "birth of a cut" transition
Abstract
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 RiemannHilbert 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.3208
 Bibcode:
 2007arXiv0711.3208M
 Keywords:

 Mathematical Physics
 EPrint:
 41 pages, 3 figures