Holroyd, AE;
Soo, T;
(2013)
Insertion and deletion tolerance of point processes.
Electronic Journal of Probability
, 18
, Article 74. 10.1214/EJP.v18-2621.
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Abstract
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.
| Type: | Article |
|---|---|
| Title: | Insertion and deletion tolerance of point processes |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1214/EJP.v18-2621 |
| Publisher version: | https://doi.org/10.1214/EJP.v18-2621 |
| Language: | English |
| Additional information: | This work is licensed under a Creative Commons Attribution 3.0 License (https://creativecommons.org/licenses/by/3.0/). |
| Keywords: | point process; finite energy condition; stable matching; continuum percolation |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10089084 |
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