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Multiple trapping of random walkers on periodic lattices

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Abstract

Formulas are obtained for the mean absorption time of a set ofk independent random walkers on periodic space lattices containingq traps. We consider both discrete (here we assume simultaneous stepping) and continuous-time random walks, and find that the mean lifetime of the set of walkers can be obtained, via a convolution-type recursion formula, from the generating function for one walker on the perfect lattice. An analytical solution is given for symmetric walks with nearest neighbor transitions onN-site rings containing one trap (orq equally spaced traps), for both discrete and exponential distribution of stepping times. It is shown that, asN → ∞, the lifetime of the walkers is of the form TakN2, whereT is the average time between steps. Values ofa k, 2 ⩽ Sk ⩽ 6, are provided.

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Authors and Affiliations

  1. División de Estudios Superiores, Facultad de Quimica, Universidad Nacional Autónoma de México, Mexico

    Alberto Robledo & Luis Woodhouse

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  1. Alberto Robledo
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  2. Luis Woodhouse
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Robledo, A., Woodhouse, L. Multiple trapping of random walkers on periodic lattices. J Stat Phys 19, 129–147 (1978). https://doi.org/10.1007/BF01012507

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