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Point processes on spaces of flats and other homogeneous spaces

Published online by Cambridge University Press:  24 October 2008

F. Papangelou
F. Papangelou
Affiliation:
University of Manchester
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Extract

The present paper is primarily concerned with the structure of certain random sets of flats in n-dimensional Euclidean space Rn. To be more specific, let be the space of k-dimensional affine subspaces of Rn (to be called k-flats below), equipped with its natural topology ((14), p. 132). is a topological homogeneous space under the action of the group of Euclidean displacements in Rn and our purpose is to give conditions under which a stochastic point process on , stationary under , is a doubly stochastic Poisson process. The results will be seen to apply equally well to abstract spaces sharing some of the structural properties of .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 80 , Issue 2 , September 1976 , pp. 297 - 314
Copyright
Copyright © Cambridge Philosophical Society 1976

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