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

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

2009-04-23

arxiv.org/abs/0904.3740v1

Mathematics

Probability

34 pages

Scientific paper

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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