Double scaling limit in the random matrix model: the Riemann-Hilbert approach

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We prove the existence of the double scaling limit in the unitary matrix model with quartic interaction, and we show that the correlation functions in the double scaling limit are expressed in terms of the integrable kernel determined by the psi-function for the Hastings-McLeod solution to the Painlevé II equation. The proof is based on the Riemann-Hilbert approach.
74 pages, 5 figures

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Mathematical Physics, High Energy Physics - Theory, Exactly Solvable and Integrable Systems

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http://salesiana.dossiersoluciones.com/handle/123456789/56960

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math-ph/0201003
 http://arxiv.org/abs/math-ph/0201003

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arXiv