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

By Alexei Borodin, Persi Diaconis, Jason E. Fulman. 2009

82 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Statistics and Probability

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In Algebra and Number Theory

Alexei Borodin

In Discrete Mathematics and Combinatorics

In Statistics and Probability

Citations in the corpus

Determinantal Point Processes for Machine Learning (2012, background): “…attracted a flurry of attention in the mathematics community [Borodin and Olshanski, 2000, Borodin and Soshnikov, 2003, Borodin and Rains, 2005, Borodin et al., 2010, Burton and Pemantle, 1993, Johansson, 2002, 2004, 2005a, Okounkov, 2001, Okounkov and Reshetikhin, 2003, Shirai and Takahashi,…”
Determinantal point processes (2018, background): “(x,y) = 0, x−y≥ 2, −1, x−y= 1, y−Px+1 r=1 (−1)r−1 P x=l0<l1<···<lr=y+1 Rl0,l1Rl1,l2 ···Rlr−1,lr x≤ y, where Ra,b = ρb−a(a,a+1,...,b−1). Details and applications can be found in [Bor09]. 11 6 Fock space A general construction of determinantal point processes via the Fock space formalism”