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Exchangeable pairs and Poisson approximation

Sourav Chatterjee·Persi Diaconis·Elizabeth Meckes
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Abstract

This is a survey paper on Poisson approximation using Stein's method of exchangeable pairs. We illustrate using Poisson-binomial trials and many variations on three classical problems of combinatorial probability: the matching problem, the coupon collector's problem, and the birthday problem. While many details are new, the results are closely related to a body of work developed by Andrew Barbour, Louis Chen, Richard Arratia, Lou Gordon, Larry Goldstein, and their collaborators. Some comparison with these other approaches is offered.

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Sourav Chatterjee, Persi Diaconis, Elizabeth Meckes. 2005-11-09. Exchangeable pairs and Poisson approximation. https://doi.org/10.1214/154957805100000096

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