On the singular sector of the Hermitian random matrix model in the large N limit
Exactly Solvable and Integrable Systems
2015-05-19 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1005.4773,
title = {On the singular sector of the Hermitian random matrix model in the large N limit},
author = {B. Konopelchenko and L. Martinez Alonso and E. Medina},
journal= {arXiv preprint arXiv:1005.4773},
year = {2015}
}
Comments
12 pages