  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.
