Isolated nearest neighbors
- 1 June 1982
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 19 (02) , 444-449
- https://doi.org/10.1017/s0021900200022956
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 ℝ v . Similar results are obtained for some related models, incidentally solving a problem proposed by D. P. Shine.Keywords
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