Electronic Journal of Probability

Insertion and deletion tolerance of point processes

Alexander Holroyd and Terry Soo

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We develop a theory of insertion and deletion tolerance for point processes. A process is insertion-tolerant if adding a suitably chosen random point results in a point process that is absolutely continuous in law with respect to the original process. This condition and the related notion of deletion-tolerance are extensions of the so-called finite energy condition for discrete random processes. We prove several equivalent formulations of each condition, including versions involving Palm processes. Certain other seemingly natural variants of the conditions turn out not to be equivalent. We illustrate the concepts in the context of a number of examples, including Gaussian zero processes and randomly perturbed lattices, and we provide applications to continuum percolation and stable matching.

Article information

Electron. J. Probab., Volume 18 (2013), paper no. 74, 24 pp.

Accepted: 11 August 2013
First available in Project Euclid: 4 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G55: Point processes

point process finite energy condition stable matching continuum percolation

This work is licensed under a Creative Commons Attribution 3.0 License.


Holroyd, Alexander; Soo, Terry. Insertion and deletion tolerance of point processes. Electron. J. Probab. 18 (2013), paper no. 74, 24 pp. doi:10.1214/EJP.v18-2621. https://projecteuclid.org/euclid.ejp/1465064299

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