Shuffling algorithm for boxed plane partitions

Abstract

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.

10 figures, 34 pages

References in corpus (2)

• Asymptotics of Plancherel-type random partitions
• On the Shuffling Algorithm for Domino Tilings

Cited by in corpus (9)

• Asymptotics of uniformly random lozenge tilings of polygons. Gaussian free field
• Bulk universality for random lozenge tilings near straight boundaries and for tensor products
• Limits of Multilevel TASEP and similar processes
• q-Distributions on boxed plane partitions
• Asymptotics of Random Lozenge Tilings via Gelfand-Tsetlin Schemes
• Elliptically Distributed Lozenge Tilings of a Hexagon
• Multilevel Dyson Brownian motions via Jack polynomials
• Representations of classical Lie groups and quantized free convolution
• Difference operators and determinantal point processes