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

## TL;DR

This paper demonstrates that in 2D simplicial gravity, the scaling limit of the correlation functions remains universal despite differences in discretized formulas, offering an alternative way to define volume correlations in 2D quantum gravity.

## Contribution

It provides a new derivation showing the universality of correlation functions in 2D simplicial gravity and proposes an alternative definition of volume-volume correlator.

## Key findings

- Scaling limit of correlation functions is universal across discretizations.
- Discretized formulas differ but lead to the same continuum behavior.
- Offers an alternative definition for Euclidean quantum gravity correlators in 2D.

## 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 $2d$.