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Random walks on lattices with points of two colours. I

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  • Den Hollander, W.Th.F.
  • Kasteleyn, P.W.

Abstract

This paper is concerned with random walks on lattices with two kinds of points, black and white. The colours of the points are random variables with a translation invariant, but otherwise arbitrary, joint probability distribution. The steps of the walk are independent of the colours. We study the stochastic properties of the length of the subwalk from the starting point to a first black point and of subwalks between points visited in succession, and establish a number of exact relations. These relations can be applied to a trapping problem by identifying the black points with imperfect traps. An example is discussed.

Suggested Citation

  • Den Hollander, W.Th.F. & Kasteleyn, P.W., 1983. "Random walks on lattices with points of two colours. I," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 117(1), pages 179-188.
    • Handle: RePEc:eee:phsmap:v:117:y:1983:i:1:p:179-188
    DOI: 10.1016/0378-4371(83)90029-8
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    References listed on IDEAS

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    1. den Hollander, W.Th.F. & Kasteleyn, P.W., 1982. "Random walks with ‘spontaneous emission’ on lattices with periodically distributed imperfect traps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 112(3), pages 523-543.
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