Ahlfors regular conformal dimension of metrics on infinite graphs coincides with the critical exponent of p-energies and relates to the spectral dimension of the graph.
Murugan, Quasisymmetric uniformization and heat kernel estimates
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Ahlfors Regular Conformal Dimension of Metrics on Infinite Graphs and Spectral Dimension of the Associated Random Walks
Ahlfors regular conformal dimension of metrics on infinite graphs coincides with the critical exponent of p-energies and relates to the spectral dimension of the graph.