Method of images for one-dimensional discrete random walk under a reflecting barrier
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915378438864896 |
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| author | Seki, Kazuhiko |
| author_facet | Seki, Kazuhiko |
| contents | The transition probability for a one-dimensional discrete symmetric random walk under a reflecting barrier was once given by the method of images. [S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943).] However, several inconsistencies have been reported when the method of images is applied in cases where a reflecting barrier is considered, even after the exact solution has been obtained. Here, we explicitly show that the method of images becomes applicable if the image position is shifted. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00926 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Method of images for one-dimensional discrete random walk under a reflecting barrier Seki, Kazuhiko Statistical Mechanics The transition probability for a one-dimensional discrete symmetric random walk under a reflecting barrier was once given by the method of images. [S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943).] However, several inconsistencies have been reported when the method of images is applied in cases where a reflecting barrier is considered, even after the exact solution has been obtained. Here, we explicitly show that the method of images becomes applicable if the image position is shifted. |
| title | Method of images for one-dimensional discrete random walk under a reflecting barrier |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2408.00926 |