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

Abstract

The singular sector of zero genus case for the Hermitian random matrix model in the large N limit is analyzed. It is proved that the singular sector of the hodograph solutions for the underlying dispersionless Toda hierarchy and the singular sector of the 1-layer Benney (classical long wave equation) hierarchy are deeply connected. This property is due to the fact that the hodograph equations for both hierarchies describe the critical points of solutions of Euler-Poisson-Darboux equations E(a,a), with a=-1/2 for the dToda hierarchy and a=1/2 for the 1-layer Benney hierarchy.

12 pages

References in corpus (3)

• Lectures on random matrix models. The Riemann-Hilbert approach
• The double scaling limit method in the Toda hierarchy
• Semiclassical expansions in the Toda hierarchy and the hermitian matrix model

Cited by in corpus (6)

• Quasi-classical approximation in vortex filament dynamics. Integrable systems, gradient catastrophe and flutter
• Singular sectors of the 1-layer Benney and dToda systems and their interrelations
• Critical points, Lauricella functions and Whitham-type equations
• Elliptic Euler-Poisson-Darboux equation, critical points and integrable systems
• Spectral curves in gauge/string dualities: integrability, singular sectors and regularization
• Unfolding of singularities and differential equations