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XXII.—Random Paths in Two and Three Dimensions

Published online by Cambridge University Press:  15 September 2014

W. H. McCrea  and
F. J. W. Whipple
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Extract

1. In a previous note (McCrea, 1936) the following problem was enunciated: A rectangular lattice is given; a particle P moves from one lattice-point to another in such a way that, when it is at any interior point, it is equally likely to move to any of its four neighbouring points. P is liberated at any given lattice-point and it is required to find the probability that it will ultimately reach any stated point in the boundary of the lattice, assuming that on arrival at a boundary point its movement ceases.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 60 , Issue 3 , 1940 , pp. 281 - 298
Copyright
Copyright © Royal Society of Edinburgh 1940

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References

References to Literature

Courant, R., Friedrichs, K., and Lewy, H., 1928. “Differenzengleichungen der mathematischen Physik,” Math. Ann., vol. c, pp. 32–74, Part I, § 3.CrossRefGoogle Scholar
McCrea, W. H., 1936. “A problem on random paths,” Math. Gaz., vol. xx, pp. 311–317.CrossRefGoogle Scholar