Translator Disclaimer
2018 Point-shift foliation of a point process
Francois Baccelli, Mir-Omid Haji-Mirsadeghi
Electron. J. Probab. 23(none): 1-25 (2018). DOI: 10.1214/17-EJP123


A point-shift $F$ maps each point of a point process $\Phi $ to some point of $\Phi $. For all translation invariant point-shifts $F$, the $F$-foliation of $\Phi $ is a partition of the support of $\Phi $ which is the discrete analogue of the stable manifold of $F$ on $\Phi $. It is first shown that foliations lead to a classification of the behavior of point-shifts on point processes. Both qualitative and quantitative properties of foliations are then established. It is shown that for all point-shifts $F$, there exists a point-shift $F_\bot $, the orbits of which are the $F$-foils of $\Phi $, and which is measure-preserving. The foils are not always stationary point processes. Nevertheless, they admit relative intensities with respect to one another.


Download Citation

Francois Baccelli. Mir-Omid Haji-Mirsadeghi. "Point-shift foliation of a point process." Electron. J. Probab. 23 1 - 25, 2018.


Received: 30 October 2016; Accepted: 4 November 2017; Published: 2018
First available in Project Euclid: 23 February 2018

zbMATH: 06868364
MathSciNet: MR3771756
Digital Object Identifier: 10.1214/17-EJP123

Primary: 37C85, 60G10, 60G55, 60G57


Vol.23 • 2018
Back to Top