Abstract
A method of studing of double scaling limits for the two-dimensional string models of quantum gravity is stated. It is actually shown that the study of such limits reduces to the isomonodromic deformation method for integrable discrete equations. A relationship is indicated between the “universality” and isomonodromy properties of the model. It is shown that the partition function of the model is the τ-function associated with the fourth Painleve equation (ℙ4), and also the Volterra chain. We consider in detail the properties of the Backlund transformations for ℙ4. Bibliography: 19 titles.
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