Universality in the Critical Behavior of the Correlation Functions in 2d Simplicial Gravity

Abstract

The analogue of the loop-loop correlation function in 2d gravity for the planar connected $\phi^3$ diagrams is calculated. It is shown that although the discretized formulas are different the scaling limit is the same as for the loop-loop correlation function. The derivation may serve as an alternative definition of the volume-volume correlator of Euclidean quantum gravity in $2d$.