Ahlfors Regular Conformal Dimension of Metrics on Infinite Graphs and Spectral Dimension of the Associated Random Walks

2020/09/08 by Kôhei Sasaya, Sasaya, Kôhei
Computer Science · Mathematics · #30L10 #60J10 #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Probability (math.PR) #Topological and Geometric Data Analysis

paper · doi:10.48550/arxiv.2009.03595

openalex publication_date 2020/09/08 · openalex created_date 2022/08/30 · openalex updated_date 2026/07/28

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.

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