From Trees to Gravity

In this article we study two related models of quantum geometry: generic random trees and two-dimensional causal triangulations. The Hausdorff and spectral dimensions that arise in these models are calculated and their relationship with the structure of the underlying random geometry is explored. Modifications due to interactions with matter fields are also briefly discussed. The approach to the subject is that of classical statistical mechanics and most of the tools come from probability and graph theory.Comment: This is a contribution to the Handbook of Quantum Gravity which will be published in the beginning of 2023. It will appear as a chapter in the section of the handbook entitled Causal Dynamical Triangulation