For a quenched trap model, the disorder-averaged particle packet decays with a universal Laplace-like tail set by the first moments of the escape rates.
Method of images for one-dimensional discrete random walk under a reflecting barrier
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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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Diffusion in Quenched Random Environments: Reviving Laplace's First Law of Errors
For a quenched trap model, the disorder-averaged particle packet decays with a universal Laplace-like tail set by the first moments of the escape rates.