Determination of the Walk Dimension of the Sierpi\'nski Gasket Without Using Diffusion

TL;DR

This paper establishes the walk dimension of the Sierpiński gasket through a novel approach that avoids diffusion, by constructing non-local Dirichlet forms from those on the Sierpiński graph.

Contribution

It introduces a new method to determine the walk dimension without relying on diffusion, using Dirichlet forms on related graphs.

Findings

Walk dimension of the Sierpiński gasket determined

Constructed non-local Dirichlet forms from graph forms

Method avoids traditional diffusion-based analysis

Abstract

We determine the walk dimension of the Sierpi\'nski gasket without using diffusion. We construct non-local regular Dirichlet forms on the Sierpi\'nski gasket from regular Dirichlet forms on the Sierpi\'nski graph whose suitable boundary is the Sierpi\'nski gasket.