Emergence of the circle in a statistical model of random cubic graphs

@article{Kelly2020EmergenceOT,
  title={Emergence of the circle in a statistical model of random cubic graphs},
  author={Christy Kelly and Carlo A. Trugenberger and Fabio Biancalana},
  journal={Classical and Quantum Gravity},
  year={2020},
  volume={38}
}
We consider a formal discretisation of Euclidean quantum gravity defined by a statistical model of random 3-regular graphs and making using of the Ollivier curvature, a coarse analogue of the Ricci curvature. Numerical analysis shows that the Hausdorff and spectral dimensions of the model approach 1 in the joint classical-thermodynamic limit and we argue that the scaling limit of the model is the circle of radius r, Sr1 . Given mild kinematic constraints, these claims can be proven with full… 

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