Open Access
2013 Insertion and deletion tolerance of point processes
Alexander Holroyd, Terry Soo
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Electron. J. Probab. 18: 1-24 (2013). DOI: 10.1214/EJP.v18-2621


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.


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Alexander Holroyd. Terry Soo. "Insertion and deletion tolerance of point processes." Electron. J. Probab. 18 1 - 24, 2013.


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

zbMATH: 1291.60101
MathSciNet: MR3091720
Digital Object Identifier: 10.1214/EJP.v18-2621

Primary: 60G55

Keywords: continuum percolation , finite energy condition , point process , Stable matching

Vol.18 • 2013
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