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arXiv · 2502.14839

The law of thin processes: a law of large numbers for point processes

Matthew Aldridge
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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 point process as n tends to infinity. 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 Harremo\"es et al.

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Matthew Aldridge. 2025-02-20. The law of thin processes: a law of large numbers for point processes. https://doi.org/10.1016/j.spl.2026.110653

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