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A simple calculation for the average number of steps to trapping in lattice random walks

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Abstract

We show that the asymptotic results for the average number of steps to trapping at an irreversible trapping site on aD-dimensional finite lattice can be obtained from the generating function for random walks on aninfinite perfect lattice. This introduces a significant simplification into such calculations. An interesting corollary of these calculations is the conclusion that a random walker traverses, on the average, all the distinct nontrapping lattice sites before arriving on the trapping site.

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This work was supported in part by NSF Grants MPS72-04363-A03 and CHE75-20624.

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Shuler, K.E., Silver, H. & Lindenberg, K. A simple calculation for the average number of steps to trapping in lattice random walks. J Stat Phys 15, 393–397 (1976). https://doi.org/10.1007/BF01020341

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  • DOI: https://doi.org/10.1007/BF01020341

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