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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn042, 51 pages, doi:10.1093/imrn/rnn042 published on April 25, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

The Riemann–Hilbert Approach to Double Scaling Limit of Random Matrix Eigenvalues Near the "Birth of a Cut" Transition

Man Yue Mo

School of Mathematics, University of Bristol, Bristol BS8 1TW, UK

Correspondence: Correspondence to be sent to: m.mo{at}bristol.ac.uk

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–x2{nu}, where {nu} is a positive integer. This provides a rigorous proof of the previous results in [18], 2006, Eynard, Journal of Statistical Mechanics, 7)


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