Probability Surveys

Exchangeable pairs and Poisson approximation

Sourav Chatterjee, Persi Diaconis, and Elizabeth Meckes

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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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Probab. Surveys, Volume 2 (2005), 64-106.

First available in Project Euclid: 28 February 2005

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Chatterjee, Sourav; Diaconis, Persi; Meckes, Elizabeth. Exchangeable pairs and Poisson approximation. Probab. Surveys 2 (2005), 64--106. doi:10.1214/154957805100000096.

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