大N极限下Hermite随机矩阵模型的奇异扇区
On the singular sector of the Hermitian random matrix model in the large N limit
摘要：
分析了Hermitian随机矩阵模型在大N极限下零亏格情形的奇异扇区。证明了无色散Toda方程族的速端图解的奇异扇区与1层Benney方程族的奇异扇区是深连通的.这一性质是由于这两个方程族的速端图方程描述了Euler-Poisson-Darboux方程E（a，a）解的临界点，其中对于dToda方程族a=-1/2，对于1层Benney方程族a=1/2。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
