Self-repelling walk on the Sierpiniski gasket
We construct a one-parameter family of self-repelling processes on the Sierpiński gasket, by taking continuum limits of self-repelling walks on the pre-Sierpiński gaskets. We prove that our model interpolates between the Brownian motion and the self-avoiding process on the Sierpiński gasket. Namely,...
| 主要な著者: | , , |
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| フォーマット: | Journal article |
| 言語: | English |
| 出版事項: |
2002
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| _version_ | 1826292238718599168 |
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| author | Hambly, B Hattori, K Hattori, T |
| author_facet | Hambly, B Hattori, K Hattori, T |
| author_sort | Hambly, B |
| collection | OXFORD |
| description | We construct a one-parameter family of self-repelling processes on the Sierpiński gasket, by taking continuum limits of self-repelling walks on the pre-Sierpiński gaskets. We prove that our model interpolates between the Brownian motion and the self-avoiding process on the Sierpiński gasket. Namely, we prove that the process is continuous in the parameter in the sense of convergence in law, and that the order of Hölder continuity of the sample paths is also continuous in the parameter. We also establish a law of the iterated logarithm for the self-repelling process. Finally we show that this approach yields a new class of one-dimensional self-repelling processes. |
| first_indexed | 2024-03-07T03:11:36Z |
| format | Journal article |
| id | oxford-uuid:b4632622-4ab7-4a07-900a-25a96e9d12ed |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:11:36Z |
| publishDate | 2002 |
| record_format | dspace |
| spelling | oxford-uuid:b4632622-4ab7-4a07-900a-25a96e9d12ed2022-03-27T04:25:44ZSelf-repelling walk on the Sierpiniski gasketJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b4632622-4ab7-4a07-900a-25a96e9d12edEnglishSymplectic Elements at Oxford2002Hambly, BHattori, KHattori, TWe construct a one-parameter family of self-repelling processes on the Sierpiński gasket, by taking continuum limits of self-repelling walks on the pre-Sierpiński gaskets. We prove that our model interpolates between the Brownian motion and the self-avoiding process on the Sierpiński gasket. Namely, we prove that the process is continuous in the parameter in the sense of convergence in law, and that the order of Hölder continuity of the sample paths is also continuous in the parameter. We also establish a law of the iterated logarithm for the self-repelling process. Finally we show that this approach yields a new class of one-dimensional self-repelling processes. |
| spellingShingle | Hambly, B Hattori, K Hattori, T Self-repelling walk on the Sierpiniski gasket |
| title | Self-repelling walk on the Sierpiniski gasket |
| title_full | Self-repelling walk on the Sierpiniski gasket |
| title_fullStr | Self-repelling walk on the Sierpiniski gasket |
| title_full_unstemmed | Self-repelling walk on the Sierpiniski gasket |
| title_short | Self-repelling walk on the Sierpiniski gasket |
| title_sort | self repelling walk on the sierpiniski gasket |
| work_keys_str_mv | AT hamblyb selfrepellingwalkonthesierpiniskigasket AT hattorik selfrepellingwalkonthesierpiniskigasket AT hattorit selfrepellingwalkonthesierpiniskigasket |