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

2025/02/20 by Matthew Aldridge, Aldridge, Matthew · 1 voice · 1 citation
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.2502.14839

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 Harremoës et al.

Cited by

• Discrete broadly stable distributions

Discussions

• … Anyway, over the last few weeks I’ve been struggling to find a reference for a certain limit theorem about point processes. So I’ve uploaded a proof of it to the arXiv, and will wait for all the out [bsky, 4 points, 3 comments]

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