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

页码：867 / 872

页数：6

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