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

被引：6
|
作者：
Konopelchenko, B. [2 ,3 ]
Martinez Alonso, L. [4 ]
Medina, E. [1 ]
机构：
[1] Univ Cadiz, Dept Matemat, E-11510 Cadiz, Spain
[2] Univ Salento, Dipartimento Fis, I-73100 Lecce, Italy
[3] Sezione Ist Nazl Fis Nucl, I-73100 Lecce, Italy
[4] Univ Complutense, Dept Fis Teor 2, E-28040 Madrid, Spain
来源：
PHYSICS LETTERS A | 2011年 / 375卷 / 05期
关键词：
Integrable systems; Hodograph equations; Random matrix models; Euler-Poisson-Darboux equation; NONLINEAR SCHRODINGER-EQUATION; WHITHAM EQUATIONS; HIERARCHY; GRAVITY;
D O I：
10.1016/j.physleta.2010.12.055
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
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. (C) 2010 Elsevier B.V. All rights reserved.
引用
收藏
页码：867 / 872
页数：6
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