Determination of the Walk Dimension of the Sierpiński Gasket Without Using Diffusion

Abstract

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

arXiv comment26 pages

Cited by in corpus (2)

• Random walks and induced Dirichlet forms on self-similar sets
• Equivalent Semi-Norms of Non-Local Dirichlet Forms on the Sierpiński Gasket and Applications