Publication: On the singular sector of the Hermitian random matrix model in the large N limit
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2011-01-31
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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.
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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
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