From Trees to Gravity
Bergfinnur Durhuus, Thordur Jonsson, John Wheater

TL;DR
This paper investigates quantum geometric models, specifically random trees and causal triangulations, calculating their dimensions and exploring how matter interactions influence their structure using probabilistic and graph theory methods.
Contribution
It provides new calculations of Hausdorff and spectral dimensions for these models and explores their relationship with the underlying geometry, including effects of matter fields.
Findings
Hausdorff and spectral dimensions are computed for the models
The relationship between geometry and dimensions is analyzed
Interactions with matter fields are briefly discussed
Abstract
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.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Quantum Mechanics and Applications · Advanced Mathematical Theories and Applications
