Geodesic
Continious limit for hermitian matrix model $\Phi^6$
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 12, Tome 187 (1991), pp. 40-52

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Double scaling limit of hermitian matrix model $\Phi^6$ to the first Painlevé equation ($\mathbb{P}_1$) and the next higher equation in $\mathbb{P}_1$ hierarchy ($\mathbb{P}_1^2$) is studied. In the first case is proved to obtain the desired limit the contour of integration must be modified. In the second case is shown that the limit exists without any modification. 
@article{ZNSL_1991_187_a2,
     author = {A. R. Its and A. V. Kitaev},
     title = {Continious limit for hermitian matrix model $\Phi^6$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {40--52},
     publisher = {mathdoc},
     volume = {187},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1991_187_a2/}
}
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A. R. Its; A. V. Kitaev. Continious limit for hermitian matrix model $\Phi^6$. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 12, Tome 187 (1991), pp. 40-52. http://geodesic.mathdoc.fr/item/ZNSL_1991_187_a2/