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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

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


Authors: Alexei Borodin, Persi Diaconis and Jason Fulman
Journal: Bull. Amer. Math. Soc. 47 (2010), 639-670
MSC (2010): Primary 05E15, 60B15
Published electronically: August 3, 2010
MathSciNet review: 2721041
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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.


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Additional Information

Alexei Borodin
Affiliation: Department of Mathematics, Caltech, Pasadena, California, 91125

Persi Diaconis
Affiliation: Departments of Mathematics and Statistics, Stanford, Palo Alto, California, 94305

Jason Fulman
Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California, 90089

DOI: http://dx.doi.org/10.1090/S0273-0979-2010-01306-9
PII: S 0273-0979(2010)01306-9
Received by editor(s): May 1, 2009
Published electronically: August 3, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.