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Random walks on lattices with randomly distributed traps I. The average number of steps until trapping

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Abstract

For a random walk on a lattice with a random distribution of traps we derive an asymptotic expansion valid for smallq for the average number of steps until trapping, whereq is the probability that a lattice point is a trap. We study the case of perfect traps (where the walk comes to an end) and the extension obtained by letting the traps be imperfect (i.e., by giving the walker a finite probability to remain free when stepping on a trap). Several classes of random walks of varying dimensionality are considered and special care is taken to show that the expansion derived is exact up to and including the last term calculated. The numerical accuracy of the expansion is discussed.

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  1. Instituut-Lorentz voor Theoretische Natuurkunde, Nieuwsteeg 18, 2311, SB Leiden, The Netherlands

    W. Th. F. den Hollander

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den Hollander, W.T.F. Random walks on lattices with randomly distributed traps I. The average number of steps until trapping. J Stat Phys 37, 331–367 (1984). https://doi.org/10.1007/BF01011838

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