Shuffling algorithm for boxed plane partitions

Details Shuffling algorithm for boxed plane partitions Shuffling algorithm for boxed plane partitions

2008-04-18

arxiv.org/abs/0804.3071v2

Advances in Mathematics, 220 (2009), no. 6, 1739-1770

Mathematics

Combinatorics

10 figures, 34 pages

Scientific paper

We introduce discrete time Markov chains that preserve uniform measures on boxed plane partitions. Elementary Markov steps change the size of the box from (a x b x c) to ((a-1) x (b+1) x c) or ((a+1) x (b-1) x c). Algorithmic realization of each step involves O((a+b)c) operations. One application is an efficient perfect random sampling algorithm for uniformly distributed boxed plane partitions. Trajectories of our Markov chains can be viewed as random point configurations in the three-dimensional lattice. We compute the bulk limits of the correlation functions of the resulting random point process on suitable two-dimensional sections. The limiting correlation functions define a two-dimensional determinantal point processes with certain Gibbs properties.

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