Aldridge, M. orcid.org/0000-0002-9347-1586 (2026) The law of thin processes: A law of large numbers for point processes. Statistics & Probability Letters, 232. 110653. ISSN: 0167-7152
Abstract
If you take a superposition of n IID copies of a point process and thin that by a factor of 1 / n , then the resulting process tends to a Poisson process as n → ∞ . We give a simple proof of this result that highlights its similarity to the law of large numbers and to the law of thin numbers of Harremoës et al.
Metadata
| Item Type: | Article |
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| Authors/Creators: |
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| Copyright, Publisher and Additional Information: | © 2026 The Author. This is an open access article under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
| Keywords: | Point processes; Poisson process; Law of large numbers |
| Dates: |
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| Institution: | The University of Leeds |
| Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) |
| Date Deposited: | 12 Feb 2026 10:55 |
| Last Modified: | 12 Feb 2026 10:55 |
| Status: | Published |
| Publisher: | Elsevier |
| Identification Number: | 10.1016/j.spl.2026.110653 |
| Related URLs: | |
| Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:237878 |
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