arXiv 0804.30712008-04math.COmath-phmath.MPmath.PR

Shuffling algorithm for boxed plane partitions

Alexei Borodin, Vadim Gorin

备注：: 10 figures, 34 pages
发表信息：: Advances in Mathematics, 220 (2009), no. 6, 1739-1770

英文摘要：

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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