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On the singular sector of the Hermitian random matrix model in the large N limit

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Konopelchenko, Boris and Martínez Alonso, Luis and Medina Reus, Elena (2011) On the singular sector of the Hermitian random matrix model in the large N limit. Physics letters A, 375 (5). pp. 867-872. ISSN 0375-9601

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Official URL: http://dx.doi.org/10.1016/j.physleta.2010.12.055




Abstract

The one-cut case of the Hermitian random matrix model in the large N limit is considered. Its singular sector in the space of coupling constants is analyzed from the point of view of the hodograph equations of the underlying dispersionless Toda hierarchy. A deep connection with the singular sector of the hodograph equations of the 1-layer Benney (classical long wave equation) hierarchy is stablished. This property is a consequence of the fact that the hodograph equations for both hierarchies describe the critical points of solutions of Euler- Poisson-Darboux equations.


Item Type:Article
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©2010 Elsevier B.V. All rights reserved.
The authors wish to thank the Spanish Ministerio de Educación y Ciencia (research project FIS2008-00200/FIS) for its finantial support. B. K. is thankful to the Departamento de Física Teórica II for the kind hospitality

Uncontrolled Keywords:Integrable systems; Hodograph equations; Random matrix models; Euler-Poisson-Darboux equation
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:34203
Deposited On:06 Nov 2015 17:05
Last Modified:10 Dec 2018 15:09

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