Shuffling algorithm for boxed plane partitions

Understand

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.