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A counterexample to R. Davidson's conjecture on line processes

Published online by Cambridge University Press:  24 October 2008

Olav Kallenberg
Olav Kallenberg
Affiliation:
Department of Mathematics, Fack, S-402 20 Göteborg 5, Sweden
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Abstract

Rollo Davidson conjectured in 1968 that every stationary second order line process in the plane which has a.s. no parallel lines is necessarily a Cox (or doubly stochastic Poisson) process. This conjecture is disproved here. An affirmative answer is further given to the question whether there exists a lattice type point process in the plane which is stationary under arbitrary area preserving affine transformations.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 82 , Issue 2 , September 1977 , pp. 301 - 307
Copyright
Copyright © Cambridge Philosophical Society 1977

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References

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