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Brownian motion on the golden ratio Sierpinski gasket
Published online by Cambridge University Press: 03 April 2023
Abstract
We construct a strongly local regular Dirichlet form on the golden ratio Sierpinski gasket, which is a self-similar set without a finitely ramified cell structure, via a study on the trace of an electrical network on an infinite graph. The Dirichlet form is the unique one that is self-similar in the sense of an infinite iterated function system, and is decimation invariant with respect to a graph-directed construction. The proof is based on a fixed point problem of a renormalization map, inspired by Sabot's celebrated work for finitely ramified fractals. Lastly, the Hunt process associated with the Dirichlet form satisfies a two-sided sub-Gaussian heat kernel estimate.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 154 , Issue 3 , June 2024 , pp. 699 - 726
- Copyright
- Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh