Probability Surveys

Exchangeable pairs and Poisson approximation

Sourav Chatterjee, Persi Diaconis, and 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.

Article information

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

Dates
First available in Project Euclid: 28 February 2005

Permanent link to this document
http://projecteuclid.org/euclid.ps/1109608868

Digital Object Identifier
doi:10.1214/154957805100000096

Mathematical Reviews number (MathSciNet)
MR2121796

Zentralblatt MATH identifier
1189.60072

Citation

Chatterjee, Sourav; Diaconis, Persi; Meckes, Elizabeth. Exchangeable pairs and Poisson approximation. Probability Surveys 2 (2005), 64--106. doi:10.1214/154957805100000096. http://projecteuclid.org/euclid.ps/1109608868.


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