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Published October 2010 | Published
Journal Article Open

On adding a list of numbers (and other one-dependent determinantal processes)

Abstract

Adding a column of numbers produces "carries" along the way. We show that random digits produce a pattern of carries with a neat probabilistic description: the carries form a one-dependent determinantal point process. This makes it easy to answer natural questions: How many carries are typical? Where are they located? We show that many further examples, from combinatorics, algebra and group theory, have essentially the same neat formulae, and that any one-dependent point process on the integers is determinantal. The examples give a gentle introduction to the emerging fields of one-dependent and determinantal point processes.

Additional Information

© 2010 American Mathematical Society. Reverts to public domain 28 years from publication. Received by the editors May 1, 2009. Article electronically published on August 3, 2010. Borodin was partially supported by NSF grant DMS 0707163. Diaconis was partially supported by NSF grant DMS 0505673. Fulman was partially supported by NSF grant DMS 0802082 and NSA grant H98230-08-1-0133. We thank David Eisenbud, Don Knuth, and Peter Winkler for useful comments.

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