Convergence to Equilibrium of Biased Plane Partitions
We study a single-flip dynamics for the monotone surface in (2 + 1) dimensions obtained from a boxed plane partition. The surface is analyzed as a system of non-intersecting simple paths. When the flips have a non-zero bias we prove that there is a positive spectral gap uniformly in the boundary conditions and in the size of the system. Under the same assumptions, for a system of size M, the mixing time is shown to be of order M up to logarithmic corrections. (C) 2010 Wiley Periodicals, Inc. Random Struct. Alg., 39, 83-114, 2011
plane partitions spectral gap mixing time coupling lozenge tiling non-intersecting paths