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Isolated nearest neighbors

Published online by Cambridge University Press:  14 July 2016

David K. Pickard
David K. Pickard*
Affiliation:
Harvard University
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Abstract

For point processes, a pair of points is isolated if each is the nearest neighbor of the other, and its degree of isolation is the relative distance to the next-nearest point. The frequency with which such pairs occur and the distribution of their degree of isolation are obtained for Poisson processes in ℝv. Similar results are obtained for some related models, incidentally solving a problem proposed by D. P. Shine.

Keywords

NEAREST NEIGHBORSISOLATED PAIRSDEGREE OF ISOLATIONPOINT PROCESSESPOISSON PROCESSES
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 2 , June 1982 , pp. 444 - 449
Copyright
Copyright © Applied Probability Trust 1982 

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References

Herbert, J. (1979) Solution to Problem 650. J. Recreational Math. 11, 227.Google Scholar
Selby, S. M. (1971) Standard Mathematical Tables. Chemical Rubber Company, Cleveland.Google Scholar
Shine, D. P. (1978) Birds on a wire, Problem 650. J. Recreational Math. 10, 211.Google Scholar
Shine, D. P. (1980) Results of Competition 10. Omni Magazine 29, 108.Google Scholar