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

Fuente: arXiv
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Main Author: Sasaya, Kôhei
Format: Preprint
Published: 2020
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author Sasaya, Kôhei
author_facet Sasaya, Kôhei
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2009_03595
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Ahlfors Regular Conformal Dimension of Metrics on Infinite Graphs and Spectral Dimension of the Associated Random Walks
Sasaya, Kôhei
Probability
Metric Geometry
30L10, 60J10
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.
title Ahlfors Regular Conformal Dimension of Metrics on Infinite Graphs and Spectral Dimension of the Associated Random Walks
topic Probability
Metric Geometry
30L10, 60J10
url https://arxiv.org/abs/2009.03595