Some relation between spectral dimension and Ahlfors regular conformal dimension on infinite graphs
Probability
2026-04-06 v2
Abstract
The spectral dimension of a weighted graph is an exponent associated with the asymptotic behavior of the random walk on the graph. The Ahlfors regular conformal dimension of the graph distance is a quasisymmetric invariant, where quasisymmetry is a well-studied property of homeomorphisms between metric spaces. In this paper, we give a typical example of a fractal-like graph with and prove a sufficient condition for
Cite
@article{arxiv.2109.00851,
title = {Some relation between spectral dimension and Ahlfors regular conformal dimension on infinite graphs},
author = {Kôhei Sasaya},
journal= {arXiv preprint arXiv:2109.00851},
year = {2026}
}
Comments
27 pages, 13 figures. This article was revised to prepare for submission to a journal. In particular, the order of sections and statements was changed. Theorem 3.2 and Proposition 3.11 of the first version, which are cited in arXiv:2211.11473, were moved to Theorem 2.2 and Proposition 4.1, respectively