Brownian motion on the golden ratio Sierpinski gasket
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866914803340017664 |
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| author | Cao, Shiping Qiu, Hua |
| author_facet | Cao, Shiping Qiu, Hua |
| contents | We construct a strongly local regular Dirichlet form on the golden ratio Sierpinski gasket, which is a self-similar set without any finitely ramified cell structure, via a study on the trace of electrical networks on an infinite graph. The Dirichlet form is self-similar in the sense of an infinite iterated function system, and is decimation invariant with respect to a graph-directed construction. A theorem of uniqueness is also provided. Lastly, the associated process satisfies the two-sided sub-Gaussian heat kernel estimate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_05181 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Brownian motion on the golden ratio Sierpinski gasket Cao, Shiping Qiu, Hua Functional Analysis Probability 28A80 We construct a strongly local regular Dirichlet form on the golden ratio Sierpinski gasket, which is a self-similar set without any finitely ramified cell structure, via a study on the trace of electrical networks on an infinite graph. The Dirichlet form is self-similar in the sense of an infinite iterated function system, and is decimation invariant with respect to a graph-directed construction. A theorem of uniqueness is also provided. Lastly, the associated process satisfies the two-sided sub-Gaussian heat kernel estimate. |
| title | Brownian motion on the golden ratio Sierpinski gasket |
| topic | Functional Analysis Probability 28A80 |
| url | https://arxiv.org/abs/2010.05181 |