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Insertion and deletion tolerance of point processes
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Holroyd, Alexander E. and Soo, Terry (2013) Insertion and deletion tolerance of point processes. Electronic Journal of Probability, Volume 18 . Article number 74. doi:10.1214/EJP.v18-2621 ISSN 1083-6489.
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Official URL: http://dx.doi.org/10.1214/EJP.v18-2621
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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Library of Congress Subject Headings (LCSH): | Point processes | ||||
Journal or Publication Title: | Electronic Journal of Probability | ||||
Publisher: | University of Washington. Dept. of Mathematics | ||||
ISSN: | 1083-6489 | ||||
Official Date: | 2013 | ||||
Dates: |
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Volume: | Volume 18 | ||||
Article Number: | Article number 74 | ||||
DOI: | 10.1214/EJP.v18-2621 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Date of first compliant deposit: | 26 December 2015 | ||||
Date of first compliant Open Access: | 26 December 2015 | ||||
Funder: | Microsoft Research, Natural Sciences and Engineering Research Council of Canada (NSERC) |
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