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arXiv · 2408.00926

Method of images for one-dimensional discrete random walk under a reflecting barrier

Kazuhiko Seki
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Abstract

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.

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Kazuhiko Seki. 2024-08-01. Method of images for one-dimensional discrete random walk under a reflecting barrier. https://doi.org/10.1063/5.0266480

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