Constructs a fractal-like graph with ds < dim_ARC < 2 and proves a sufficient condition for dim_ARC ≤ ds < 2 on infinite weighted graphs.
Ahlfors Regular Conformal Dimension of Metrics on Infinite Graphs and Spectral Dimension of the Associated Random Walks
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Quasisymmetry is a well-studied property of homeomorphisms between metric spaces, and Ahlfors regular conformal dimension is a quasisymmetric invariant. In the present paper, we consider the Ahlfors regular conformal dimension of metrics on infinite graphs, and show that this notion coincides with the critical exponent of $p$-energies. Moreover, we give a relation between the Ahlfors regular conformal dimension and the spectral dimension of a graph.
years
2021 2verdicts
UNVERDICTED 2representative citing papers
Constructs dyadic cube systems in complete doubling uniformly perfect metric spaces with a three-cube chain property connecting any two points.
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Some relation between spectral dimension and Ahlfors regular conformal dimension on infinite graphs
Constructs a fractal-like graph with ds < dim_ARC < 2 and proves a sufficient condition for dim_ARC ≤ ds < 2 on infinite weighted graphs.
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Systems of Dyadic Cubes of Complete, Doubling, Uniformly Perfect Metric Spaces without Detours
Constructs dyadic cube systems in complete doubling uniformly perfect metric spaces with a three-cube chain property connecting any two points.