Calculation of string correlation functions on a hierarchical tree

String correlation functions in 2D gravity resemble similar objects in the statistical mechanics of directed polymer models on disordered trees. This analogy can be used to provide an approximate mapping between the two problems. Using such a mapping we derive renormalization group equations and calculate the ensuing scaling of the string correlation functions. We find it to agree with the results known for 2D gravity. The result further substantiates the similarity between the two models and shows that they share not only the free energy in the thermodynamic limit but also the gross structure of the correlation functions.