Probability around the Quantum Gravity. Part 1: Pure Planar Gravity

TL;DR

This paper rigorously explores stochastic dynamics that preserve quantum gravity distributions, focusing on local correlations and combinatorial methods in pure planar quantum gravity, bridging probability theory and quantum physics.

Contribution

It introduces a rigorous probabilistic framework for pure planar quantum gravity dynamics, emphasizing local correlations and combinatorial techniques over traditional matrix models.

Findings

Existence of local correlation functions in the thermodynamic limit

Properties of these correlations in pure planar quantum gravity

Rigorous combinatorial approach to quantum gravity dynamics

Abstract

In this paper we study stochastic dynamics which leaves quantum gravity equilibrium distribution invariant. We start theoretical study of this dynamics (earlier it was only used for Monte-Carlo simulation). Main new results concern the existence and properties of local correlation functions in the thermodynamic limit. The study of dynamics constitutes a third part of the series of papers where more general class of processes were studied (but it is self-contained), those processes have some universal significance in probability and they cover most concrete processes, also they have many examples in computer science and biology. At the same time the paper can serve an introduction to quantum gravity for a probabilist: we give a rigorous exposition of quantum gravity in the planar pure gravity case. Mostly we use combinatorial techniques, instead of more popular in physics random matrix models, the central point is the famous $\alpha =-7/2$ exponent.